@choibean21 the whole point of adding an integrating factor is so that the left side rule looks like the product rule for the derivative of two functions multiplied by each other. So when you work backwords...you already have the answer. It's just the integrating factor mulitplied by the function we're trying to solve. Convince yourself by differentiating the integrating factor multiplied by the function we're trying to solve.
@tadm123 we already have the solution for integrating it. The whole point of integrating factors is so that hte left side looks like the product rule for the derivative of our integrating factor multiplied by the function we're trying to solve for.
I like that you slightly pause after you are done writing something down. It gives me time to stop the video to look at what you wrote and think about it.
Also, your use of different colours is ridiculously helpful.
I've been trying to grasp this for days now. I just watched this video, did the problem in about a minute, turned around, and hit my Staples easy button.
@dfairbanks06 Try it and see what happens. If you do include the +c in the integrating factor it will end up cancelling out because after you multiply both sides by e^(something + c) that turns into e^(something) * e^c. The e^c's then just cancel because they are on both sides.
hey there, i just watch your video and gladly, i do understand now my lesson, and we have a quiz tomorrow...so if i passed that quiz..i'll definitely like this video.. >:D but if not.........i'll still have to watch your videos. XD
Just took an exam on this last week. We got our exams back today and the class average was a 55% and I got a 95% and I credit these videos for my high score. You sir are awesome.
omg i stared at that plus sign that should have been a minus sign for twenty minutes thinking if i had learned calculus all wrong (since i am reviewing) i guess i wasn't crazy after all T_T
Thank you thank you thank you!!! I've been trying to learn this for a week and I couldn't get it! This 5 minute video is better than all my lecturers and notes!
Well explained. Just to point out something, when you integrate the power of the integrating factor at 1:30 technically you should have plus c at the top and and then bring it down as a constant, since you multiply the I.F to the equation, the constants cancel out. Thats why people dont bother righting down plus C. Just thought you might want to point that out for people that dont know :)
Half the time in my calc class when my teacher is teaching us something new i always say to myself, "Ima go home later tonight and learn this via PatrickJMT" lol
your videos are great but i couldn't find something to help me solve this: (x^3 +x*y^2 -y)dy + (y^3 +y*x^2 +x)dx, i'm studying for my test (saturday) and i came up with this in a book, i hope you could help
I have a first year DE professor this term and he is not very good at teaching. Your videos helped me through all three term of Calc and these DE ones aren't any different. Thanks a lot!
is there a mistake at around1:56? i don't get how when he expands the bracket the 2nd part of the left hand side turns into +ve. i'm sure i'm wrong though :)
@PianoManX2 The trick is that he made the left side resemble the product rule. The product rule being u'v * v'u. u = e^(-x^2) and v = y. Since he made it into a derivative (by making it resemble product rule), when integrating the left side, he would be integrating a derivative. So that leaves the u*v stuff. :)
We started this section in class yesterday, and our teacher worked a very similar example. Looking at my notes, I don't know what he did. I was so confused. I see this video, and ten minutes later it is crystal clear! Thanks a lot!
Your videos have been the only reason that I've made it as far as Differential Equations. This is the last Math class that I will have to take. Thank you so much for all of your help, you've taught me almost everything I know about math.
Is this a general all-purpose method for these kinds of problems? Today our professor taught us this other much more complex method with multiple steps of solving and substituting, and if this works all the time I'll just convert to this for test time.
Wanted to let you know that your website in the description leads to the wrongs place (I think). I want everyone to be able to have a chance to see your amazing videos!
@laces124 From what I understand, the intergration of [-2xe^(-x^2)].y (remember, it's suppose to be a minus. the guy made a mistake) is in fact [e^(-x^2)].y
What I don't understand however, is where the heck did the first part go. What happen to the intergration of
[e^(-x^2)]y'? I thought the thing was intergrated in terms of x.
Only very small amount of jobs require such math skills, designing computer software in high tech industry, aerodynamic designs. Then most of it is done by computers, however, the computer software must be designed by mathematicians.
I'm using Boas "Mathematical Methods in the Physical Sciences" and I couldn't even remotely understand the way she does it. This video gave me clarity. Thanks for posting this!
@69iron69 its not that Sal "rambles" its because some people don't understand concepts as quickly as others do and his main goal is to make everyone understand exactly what hes talking about.
@MaXiiMo93 I agree for more introductory subject matter but more advanced subjects need background info anyway. If your watching calc 2 video's with out taking calc 1 you would be totally lost.
People attempt to trivialize mathematics because they find it overwhelming. Math is such a vast body of knowledge; I guess it's only natural people become frustrated with it. I remember when I was a poor algebra student, math seemed vague and incomprehensible; and I couldn't even grasp the basic idea as to why any one would want to find the "equation of a line." I was like, WTF? But once it clicks, you can actually absorb mathematical concepts much more rapidly.
@leonleon177 correct, but what we have here is xe^(-x^2), which can be integrated with a u-substitution, because xdx will be the differential needed to make this thing work out.
When you mulitply throughout by the integrating factor, the left hand side is the derivative of the integrating factor times the independent variable y.
d/dx [e^{-x^2}y]
if you integrate that with respect to x you just get ye^(-x^2).
Patrick, I love you. Seriously. I love three things in life: My mom, Fallout 3 and you. I have add and I've had huge problems with my professors lectures (I'm in a masters programme in northern Europe) only because they have a way of teaching that only really suits one kind of brain. You, on the other hand, somehow manage to make me understand things. Thank you!
@patrickJMT Your response to @gespilk was not only totally appropriate, but the best response theoretically possible. I have devised a wonderful proof of this fact, which, unfortunately, this YouTube comment is too small to contain.
Differential equations are used in the real world.
Many engineering simulators use mathematical models of subject systems in the form of differential equations. Forensic scientists use differential equations, particularily the rules of "Newton's Law of Cooling" to determine the time of death of a person. Obviously they donot take out a pen and paper, they use computer simulators but someone has to program those computer. At the least, you learn how to think critically.
Solving a differential equation is only a step to see the big picture.
Not only differential equations solving ability but also other engineering disciplines and analytical knowledge are required to get a very well paid job.
@gespilk First off, anyone who does high level physics/astronomy/mathematics/engineering/etc, has to know how to do differential/integral calculus you twit.
Secondly, college is a weeding out process. If one cannot do simple tasks such as differential equations, I would not want that person to be working for my city.
Lastly, mathematics is beautiful. If you cannot get an aesthetic feel from this, or do these problems, I really hope you work in the fast food business:p
@gespilk when you need to solve a real problem: you simplify it by creating a mathematical model. then you solve some equations and then apply the results in the real world and notice whether there have been errors.
@gespilk all good questions actually ;) Lookup "Signalling (economics)" in wikipedia, and you'll have your answer. According to the theory, managers can't observe very well your job productivity when doing creative work. They therefore select and bid for workers using other indirect metrics, like credentials. They aren't concerned so much about what you learned in college, but that you were able to go through college: which requires ambition, diligence, ability to cope with authority, etc.
@gespilk Im in electrical engineering and DEs are everywhere. In fact Im looking at the video because I came across a circuit (RC in time domain) that can be modeled by this type of DE. There are also circuits I have solved with second order linear ordinary DEs. DEs are in fact very useful; especially in circuit analysis and fluid dynamics.
its called modeling. take an electic circuit. an RC or RL circuit behaves like a first order linear differential equation. if you know how to solve a linear differential equation, you can pretty much solve any circuit. if can solve 2nd order DE. you can solve any RLC circuit... and these are just electrical engineering problems.
and how does it fit your data? you apply the real world relationship developed through experiments(for circuits KVL etc) and if you get a derivative, it fits
@moeSlow Thanks for the explanation dude, it help me understand how those kind of circuits work. But what is most important about differental equations is how it is applied in electrical and mechanical engineering
@gespilk Haha u r soo funny and totally retarded. In ur case its probably not such a good idea to educate urself. If u r like 13 years old then ignore this comment, cause then you're not expected to understand such things.
@gespilk i think u r one ignorant person, mathematics is highly used in financial modelling these days and dont u know about actuarial science? both quants and actuaries mint money like crazy...dont blv me do ur own research...:)
@gespilk Lol aw...so many people have replied to your comment. I personally still can't tell if you're joking or not. But if not, I guess you have plenty of suggestions now for a job...
@gespilk You use this type of problem solving for a number things; including, radioactive carbon dating. Something that pays much more than the amount necessary to feed your family.
@gespilk Mate you have to be the most nieve person I have ever met, jobs in finance require you to be able to be numerically fluent in order to perform quantitative research. Why do you think as part of accounting and finance degrees they must do units in maths espically focusing on calculus and algebra. That because on the path to some of the highest payin jobs (i.e. investment banking and funds management) you have to be a brilliant analyst which uses calculus techniques.
@gespilk these are used in physics and engineering, it aslo demonstrates an ability to do complex maths and solve complex problems. If you wanna work at mcdonalds then nah u should be fine without it :D
Calculus is just a tool set used to help solve problems that would be more complicated without it. Certain sciences rely strongly on calculus. If you aren't interested in getting into any of the many jobs that use it, it definitely is pretty worthless to you. I won't be using any of this for any real purpose until I start working with statistics in psychology.
Btw, a lot of textbooks give examples for how the math is used irl. (albeit over-simplified ones)
@gespilk differential equations form the very basis of our world. So they are a fundamental part of scientific studies and are used on a daily basis by scientists, engineers, mathematicians (including bankers!). im not sure to which real life system it corresponds but the point is to practice with the simple equations. Anyhow if all you want is to look after a family,. your best bet is ta career which requires ODEs
@gespilk Well if you wanted to work as an actuary, for example, to calculate probabilities of someone going from a healthy state to death in a certain time period, one of the steps involved requires first order differential equations. Obviously this information would be of value to an insurance company. They are useful in many other situations aswell
Agree sometimes it crossed my mind that what is the use of this equations if you dont know how to apply them in real life situations its really funny....but i guess you should pass this subject and be good to it for you to graduate :D
@gespilk mechanical engineering for example relies heavily on solving differential equations, as they describe the bending behavior of materials. (random example).
Does this still work the same if you have y-or-x-squared or cubed or something like that? We had this as a topic recently and the notes were somewhat unclear...
At the beginning of the video, you say to multiplty both sides by e^P(x) . . . but you seem to have meant to say to multiply both sides by e^Integral of P(x) . . .
. . . correct?
Thanks for all of your great videos. I wish you had more on Statistics.
At a first glance it bugged me that at the first integral ( exp(integral(-2x)) ) he didn't add a constant ( c ) at the end.
After a minute i remembered that the operation of integration gives you a SET of primitives (that vary from one another by a constant), so normally he chose the primitive with c=0.
@archiemedes42 C is not affected by constants but is only affected by variables. In other words, it will absorb any constants. When simplified, the equation should be:
@itaffy13 Still, at 1:30, variables are involved and he simply integrates within the exponent, and I thought a constant should pop out there because he is doing nothing more than a simple indefinite integral.
Left side integration would be a reverse product rule.... But as my professor say, it should always come out as a derivative for a product rule
liquid8oy 2 days ago
Patrickjmt when doing the left side there is supposed to be a minus sign instead of a plus sign when multiplying e to the -x squared.
ballz620 3 days ago
THANKS
ficcccRR 4 days ago
Comment removed
ficcccRR 4 days ago
I cant understand how did you integrate the left side.. im quite slow.
choibean21 5 days ago
@choibean21 the whole point of adding an integrating factor is so that the left side rule looks like the product rule for the derivative of two functions multiplied by each other. So when you work backwords...you already have the answer. It's just the integrating factor mulitplied by the function we're trying to solve. Convince yourself by differentiating the integrating factor multiplied by the function we're trying to solve.
spdyeric 4 days ago
partrickJMT > khanacademy
Spartod 1 week ago
Hm sorry but how do you integrated the left side? did you use int. by parts?
tadm123 1 week ago
@tadm123 we already have the solution for integrating it. The whole point of integrating factors is so that hte left side looks like the product rule for the derivative of our integrating factor multiplied by the function we're trying to solve for.
spdyeric 4 days ago
I like that you slightly pause after you are done writing something down. It gives me time to stop the video to look at what you wrote and think about it.
Also, your use of different colours is ridiculously helpful.
You have helped me very much. Thank you.
MissChelsie24 1 week ago
At 4:50 can you just say y = -1/2, since C divided by anything is still C?
Matthew2400 2 weeks ago
Aren't you missing a factor of -1 when you integrate the left side? cuz of the -x^2.
azndude3600 1 month ago in playlist Calculus / Second Semester - Integration
a million light bulbs just went off in my head
seaweedsupper 1 month ago
@seaweedsupper outage?
norbert010011 1 month ago
Would you possibly be able to do some videos on mechanics just I find it very difficult to learn it for my lecturer. Thanks.
MrAdamTommo 1 month ago
I've been trying to grasp this for days now. I just watched this video, did the problem in about a minute, turned around, and hit my Staples easy button.
YES.
McChickenn 2 months ago
so... you dont need to include the constant in the integrating factor? no +c?
dfairbanks06 2 months ago
@dfairbanks06 Try it and see what happens. If you do include the +c in the integrating factor it will end up cancelling out because after you multiply both sides by e^(something + c) that turns into e^(something) * e^c. The e^c's then just cancel because they are on both sides.
puref0rlyfe 1 week ago
Comment removed
megabenman 2 months ago
hey there, i just watch your video and gladly, i do understand now my lesson, and we have a quiz tomorrow...so if i passed that quiz..i'll definitely like this video.. >:D but if not.........i'll still have to watch your videos. XD
silentcrow00 2 months ago
Just took an exam on this last week. We got our exams back today and the class average was a 55% and I got a 95% and I credit these videos for my high score. You sir are awesome.
KimJong7hrill 2 months ago 20
@KimJong7hrill tell everyone about the videos! congrats on your good grade : )
patrickJMT 2 months ago 3
awesome vid, thanks!
shnepple 2 months ago
omg i stared at that plus sign that should have been a minus sign for twenty minutes thinking if i had learned calculus all wrong (since i am reviewing) i guess i wasn't crazy after all T_T
Brian626 2 months ago
Thanks man,...my savior also....Me Subscribed =D
BANANAENDMANDARINA 2 months ago
<3
Shaneyyy23 2 months ago
Thank you thank you thank you!!! I've been trying to learn this for a week and I couldn't get it! This 5 minute video is better than all my lecturers and notes!
krnl626 2 months ago
My lecturer is pretty damn good at this.
But you're better.
RanmaruKyurei 3 months ago 9
@RanmaruKyurei : )
patrickJMT 3 months ago
Well explained. Just to point out something, when you integrate the power of the integrating factor at 1:30 technically you should have plus c at the top and and then bring it down as a constant, since you multiply the I.F to the equation, the constants cancel out. Thats why people dont bother righting down plus C. Just thought you might want to point that out for people that dont know :)
krazzyKooldownKrew84 3 months ago
Great video, I'm a big fan. But I was wondering if you could explain more clearly how you integrated the left hand side around the 2:55 mark?
ronanscally 3 months ago in playlist Differential Equations
Half the time in my calc class when my teacher is teaching us something new i always say to myself, "Ima go home later tonight and learn this via PatrickJMT" lol
HirosAwp 3 months ago 17
@HirosAwp ha ; ) i have most calc stuff fortunately!
patrickJMT 3 months ago
Dr >>> U have to do some on the DIFF course
I need a way to distinguish between the types of equations
maybe more examples as well
I like , I do understand , and u make a difference in the way i deal with Maths , but I can't find this enough
DUAAQARUTEE 3 months ago
your videos are great but i couldn't find something to help me solve this: (x^3 +x*y^2 -y)dy + (y^3 +y*x^2 +x)dx, i'm studying for my test (saturday) and i came up with this in a book, i hope you could help
AnaitatZZ 3 months ago
I have a first year DE professor this term and he is not very good at teaching. Your videos helped me through all three term of Calc and these DE ones aren't any different. Thanks a lot!
AvengedxTide 4 months ago
@AvengedxTide absolutely my pleasure : ) happy to know that i have been able to help you for so many classes!
patrickJMT 4 months ago
is there a mistake at around1:56? i don't get how when he expands the bracket the 2nd part of the left hand side turns into +ve. i'm sure i'm wrong though :)
Richardhuang70 4 months ago
You sir are a good man!!!!!!!!!!!!
southpawking1 4 months ago
I still don't understand the integration of the left side.
PianoManX2 4 months ago
@PianoManX2 The trick is that he made the left side resemble the product rule. The product rule being u'v * v'u. u = e^(-x^2) and v = y. Since he made it into a derivative (by making it resemble product rule), when integrating the left side, he would be integrating a derivative. So that leaves the u*v stuff. :)
qwerty14142 4 months ago
It's very clear. However, I still have a hard time integrating this equation:
dx/dt + ax = b e^ (-ct)
I have been solving this for hours. Thank you very much.
CarlCarlosP 4 months ago
We started this section in class yesterday, and our teacher worked a very similar example. Looking at my notes, I don't know what he did. I was so confused. I see this video, and ten minutes later it is crystal clear! Thanks a lot!
propcoiscool 4 months ago
@propcoiscool no problemo!
patrickJMT 4 months ago
Your videos have been the only reason that I've made it as far as Differential Equations. This is the last Math class that I will have to take. Thank you so much for all of your help, you've taught me almost everything I know about math.
jamesbkovach 4 months ago
Thanks!!
Bartolitz 4 months ago
r u a mathematician
themythofthelegend1 4 months ago
@themythofthelegend1 nope
patrickJMT 4 months ago
If i clean that up, algebraically,
y = c
is that correct?
liu408 4 months ago
@liu408 no
y=(C/(e^-x^2)) - 1/2)
splintercellfool1 4 months ago
Comment removed
liu408 4 months ago
GOOD WORK!
ichigo0993 5 months ago
Thanks for the video. This made it very clear to understand this topic.
LEot128 5 months ago
you sir are a good man !
SamuelSherryENGR2002 5 months ago
thanks for reminding the trick! :) left side = y times Integrating factor..
tajole2323 5 months ago
thanks - good explanation!
phantasm225 5 months ago
Where did the negative in front of your P(x) go when you expanded by the integrating factor? :/
d0paminee 5 months ago 2
Thank you for the great intro to 1. order linear ODEs, patrickJMT!
shadowC10ne 5 months ago
Good job man - you´re really good :)
timugin 5 months ago
Is this a general all-purpose method for these kinds of problems? Today our professor taught us this other much more complex method with multiple steps of solving and substituting, and if this works all the time I'll just convert to this for test time.
goldenchopsticks 6 months ago
==ʍɔupʍɐı5ɯp/s/ɯoɔ˙ɹǝpɐןs˙ʍʍʍ//:dʇʇɥ ˙uıʎɐs ʇsnɾ ˙uosɹǝd ןɐǝɹ ɐ ɯ,ı puɐ ɯɐds ʇou sı sıɥʇ ˙sɹǝqɯnu ɥʇıʍ pooƃ ǝɹɐ oɥʍ ǝsoɥʇ ɹoɟ ʎǝuoɯ ʞɔınb ǝʞɐɯ oʇ ʎɐʍ ɐ sɐ ןןǝʍ sɐ sɯǝןqoɹd ɥʇɐɯ ɹnoʎ ןןɐ oʇ suoıʇɐuɐןdxǝ puɐ sɹǝʍsuɐ ǝǝɹɟ oʇ ssǝɔɔɐ ɹoɟ ʇunoɔɔɐ uɐ ǝʞɐɯ puɐ ʇɥƃıs sıɥʇ oʇ oƃ
lamrontisi713 6 months ago
who else is here because of dr. wang's class at uga??
jaffey2006 7 months ago
can someone tell me the new site of patrickjmt's videos just message me thanks ....
feelmypower2009 7 months ago
@gespilk without diff eq°, you might not be able to post your comment. this is not a mockery, but I would like to make a point too.
froet213kil 7 months ago in playlist PatrickJMT Math videos
You sir, are my savior.
Nae00 7 months ago 20
This is the type of stuff that makes me love math.
cadallac00 8 months ago 2
Wanted to let you know that your website in the description leads to the wrongs place (I think). I want everyone to be able to have a chance to see your amazing videos!
side8end 8 months ago
When you are integrating the left hand side what happens to the 2xe^-xsquared times y?
laces124 8 months ago
@laces124 From what I understand, the intergration of [-2xe^(-x^2)].y (remember, it's suppose to be a minus. the guy made a mistake) is in fact [e^(-x^2)].y
What I don't understand however, is where the heck did the first part go. What happen to the intergration of
[e^(-x^2)]y'? I thought the thing was intergrated in terms of x.
shadowanbu 8 months ago
You rock, just sayin'.
Semicolon7645 8 months ago
Only very small amount of jobs require such math skills, designing computer software in high tech industry, aerodynamic designs. Then most of it is done by computers, however, the computer software must be designed by mathematicians.
josephliang63 8 months ago
I'm using Boas "Mathematical Methods in the Physical Sciences" and I couldn't even remotely understand the way she does it. This video gave me clarity. Thanks for posting this!
AtomicElbowDrop 8 months ago
Comment removed
boala2 9 months ago
I don't know if you do need any donation. But if you do, I'm seriously willing to donate some money. Noble deeds need support! =)
atdream105 9 months ago
You just explained to me in 6 minutes what my lecturer attempted (and failed) to explain in 2 hours!
Future0ftheLeft 9 months ago
thankyou
ravikumarmistry 9 months ago
Is the left hand side always y*integrating factor for linear differential equations of order 1?
Pranikki1 9 months ago
thank you, thank you, thank you!
VargheseVlogs 9 months ago
Can you further explain how the left side integrates to I*y, I don't quite see it...
FBSnow 9 months ago 2
@FBSnow
The3musket33rs 3 months ago
Wonderful, I wish you and Khan academy could collaborate and just pump out a ton of videos!
RAF0769 9 months ago
great i know how to do it now
koenarens 9 months ago
Ah, so many times have i hear "Ok, in this video..." i begin to understand after hearing that.
trudal987 9 months ago 2
whoever comes up with these techniques is brilliant wow because they work everytime, great video by the way
caseofthefunnies 10 months ago
when i think about patrickjmt i get butterflies in my stomach yes homo
htedrom 10 months ago
your math videos are 2* as good as the khanacademy! sal just rambles on your right to the point!
good work
69iron69 10 months ago 8
@69iron69 plenty of room on the internet for all styles and viewpoints ; ) the more, the merrier!
patrickJMT 10 months ago 39
@patrickJMT True that ... bring it on ...
paperfreeck 6 months ago
@69iron69 its not that Sal "rambles" its because some people don't understand concepts as quickly as others do and his main goal is to make everyone understand exactly what hes talking about.
MaXiiMo93 8 months ago
@MaXiiMo93 I agree for more introductory subject matter but more advanced subjects need background info anyway. If your watching calc 2 video's with out taking calc 1 you would be totally lost.
69iron69 8 months ago
@69iron69 Fuck you Sal does a great job.
fuckooo 5 months ago
@fuckooo Who are you Bill Gates?
69iron69 5 months ago
where is the +C?
dajakesta1234 10 months ago
This has been flagged as spam show
i was not so clear
tayyabuuu 10 months ago
People attempt to trivialize mathematics because they find it overwhelming. Math is such a vast body of knowledge; I guess it's only natural people become frustrated with it. I remember when I was a poor algebra student, math seemed vague and incomprehensible; and I couldn't even grasp the basic idea as to why any one would want to find the "equation of a line." I was like, WTF? But once it clicks, you can actually absorb mathematical concepts much more rapidly.
IndividualParties 10 months ago
thanks a lot, totally saved me on my assignment
nowknow0123 10 months ago
do you have to multiply c by the integrating factor at the end?
anabum2 11 months ago
can you also integrate the integral of xe^-xsquared by parts?
thanks for the video! :)
elwajiola 11 months ago
The sound is a bit alien- like, nice explanation though.
BnanaXD 11 months ago
are there any partial differential equations lectures/ tutorials on youtube? thanks.
FallofDarkness55 11 months ago
OMG when i search you this on youtube, and your name came up. i acutally said thankgod patrick! LOL
VAZNH 11 months ago
Oh my goodness This was so Helpful, I missed this class and this has really been helpful for explaining how to do it
tallactor1127 11 months ago
This is like, the billionth time you've helped me with calc, so I feel obligated to say "Thank you. Very VERY much."
ZtheManiacal 11 months ago
wait what happen to that y prime?
RAE4eva666 1 year ago
patrick, e^(-x^2) does not have an antiderivative.
my math professors told me and i looked it up on wolfram alpha.
leonleon177 1 year ago
Comment removed
Moonshield15 11 months ago
Comment removed
Moonshield15 11 months ago
This has been flagged as spam show
@leonleon177 So what? We're talking about xe^(-x^2), not e^(-x^2).
Moonshield15 11 months ago
@leonleon177 correct, but what we have here is xe^(-x^2), which can be integrated with a u-substitution, because xdx will be the differential needed to make this thing work out.
msnorwoo 11 months ago
@leonleon177 e^(-x^2) doesnt, but x.e^(-x^2) does!
wazza1818 8 months ago
thank so much better than my diff eq prof
julub 1 year ago
many thanks! doing what my prof. can't do very well..
evolutionist79 1 year ago
Jackasses just got trolled.....
sid9221 1 year ago
if you can upload more about bernouli's equations
owdi2631992 1 year ago
i love you!!!!!!!!
fargalik 1 year ago
so around 3:05, the case is always the integrating factor times y?
4thKyuubi 1 year ago
im still confused about how at 2:58 the integration is that? =/
divinitiescreature 1 year ago
how would you integrate the left hand side?
divinitiescreature 1 year ago
@divinitiescreature
When you mulitply throughout by the integrating factor, the left hand side is the derivative of the integrating factor times the independent variable y.
d/dx [e^{-x^2}y]
if you integrate that with respect to x you just get ye^(-x^2).
IndividualParties 1 year ago
Patrick, marry me:D and we can study calculas all night long baby?
MrDj2976 1 year ago
And when you got the integrating factor, shouldn't you have acknowledged a constant of integration?
mariomaruf 1 year ago
My book says to identify an equation of the form y' - P(x)y = Q(x), and that would make the integrating factor Ce^x^2.
mariomaruf 1 year ago
Thank you so much for this! Have been stuck on these for ages and i understand it now!! :D
timjimtom 1 year ago
Patrick, I love you. Seriously. I love three things in life: My mom, Fallout 3 and you. I have add and I've had huge problems with my professors lectures (I'm in a masters programme in northern Europe) only because they have a way of teaching that only really suits one kind of brain. You, on the other hand, somehow manage to make me understand things. Thank you!
Audrina399 1 year ago
1) What JOBS would require to be able to CREATE and solve this equation (outside of educational system)?
2) What Real systems are represented by this equation?
3) Let's say I have some x,y data. How would I figure out that this is the equation that fits my data? try and error?
I really struggle with these questions because to feed and look after family I need a good job.
And nobody I heard of hires based on the ability to solve differential equations. They want solutions of real problems.
gespilk 1 year ago
@gespilk lol
patrickJMT 1 year ago 159
@patrickJMT Your response to @gespilk was not only totally appropriate, but the best response theoretically possible. I have devised a wonderful proof of this fact, which, unfortunately, this YouTube comment is too small to contain.
ejstheman 7 months ago
@patrickJMT pure class haha
Ninjarni 6 months ago
@gespilk ,
Differential equations are used in the real world.
Many engineering simulators use mathematical models of subject systems in the form of differential equations. Forensic scientists use differential equations, particularily the rules of "Newton's Law of Cooling" to determine the time of death of a person. Obviously they donot take out a pen and paper, they use computer simulators but someone has to program those computer. At the least, you learn how to think critically.
threetwo1234 1 year ago
@gespilk We're solving these types of problems in my calculus class. I'm currently in an electrical engineering program.
Unfortunately not everything you learn will be applied at a job, but you learn these things to give you an understanding of the bigger picture.
Metra90 1 year ago
@gespilk thats funny! lol
bebe2ful 1 year ago
@gespilk Sounds like you already failed... similar to how I'll be doing tomorrow morning...
Econ98 1 year ago
@gespilk
financial engineers solve partial differential equations and get paid a lot
warwize 1 year ago
@gespilk
- missile, rocket orbits and movements
-Electric circuits
-Heat transfer equations
-resonance and vibration behaviours
-radioactivity degradation
-population ratios
-chemical reactions
Solving a differential equation is only a step to see the big picture.
Not only differential equations solving ability but also other engineering disciplines and analytical knowledge are required to get a very well paid job.
qrrak 1 year ago
@gespilk First off, anyone who does high level physics/astronomy/mathematics/engineering/etc, has to know how to do differential/integral calculus you twit.
Secondly, college is a weeding out process. If one cannot do simple tasks such as differential equations, I would not want that person to be working for my city.
Lastly, mathematics is beautiful. If you cannot get an aesthetic feel from this, or do these problems, I really hope you work in the fast food business:p
fcdog555 1 year ago
@gespilk when you need to solve a real problem: you simplify it by creating a mathematical model. then you solve some equations and then apply the results in the real world and notice whether there have been errors.
kenyasong 1 year ago
@gespilk Hey I think you're lost, because your complaining sounds like that of a remedial algebra student.
ammatzner 1 year ago
@gespilk all good questions actually ;) Lookup "Signalling (economics)" in wikipedia, and you'll have your answer. According to the theory, managers can't observe very well your job productivity when doing creative work. They therefore select and bid for workers using other indirect metrics, like credentials. They aren't concerned so much about what you learned in college, but that you were able to go through college: which requires ambition, diligence, ability to cope with authority, etc.
UnconformistSheep 1 year ago
@gespilk Im in electrical engineering and DEs are everywhere. In fact Im looking at the video because I came across a circuit (RC in time domain) that can be modeled by this type of DE. There are also circuits I have solved with second order linear ordinary DEs. DEs are in fact very useful; especially in circuit analysis and fluid dynamics.
nitroxide17 11 months ago 2
@gespilk
its called modeling. take an electic circuit. an RC or RL circuit behaves like a first order linear differential equation. if you know how to solve a linear differential equation, you can pretty much solve any circuit. if can solve 2nd order DE. you can solve any RLC circuit... and these are just electrical engineering problems.
and how does it fit your data? you apply the real world relationship developed through experiments(for circuits KVL etc) and if you get a derivative, it fits
moeSlow 11 months ago 3
@moeSlow Thanks for the explanation dude, it help me understand how those kind of circuits work. But what is most important about differental equations is how it is applied in electrical and mechanical engineering
MKL131366 11 months ago
@gespilk Haha u r soo funny and totally retarded. In ur case its probably not such a good idea to educate urself. If u r like 13 years old then ignore this comment, cause then you're not expected to understand such things.
//Best wishes, yours truly.
Tompish 11 months ago
@gespilk i think u r one ignorant person, mathematics is highly used in financial modelling these days and dont u know about actuarial science? both quants and actuaries mint money like crazy...dont blv me do ur own research...:)
hussainkhalid 10 months ago
@gespilk Lol aw...so many people have replied to your comment. I personally still can't tell if you're joking or not. But if not, I guess you have plenty of suggestions now for a job...
nutella871 10 months ago
@gespilk You use this type of problem solving for a number things; including, radioactive carbon dating. Something that pays much more than the amount necessary to feed your family.
scottsivard 10 months ago
@gespilk Mate you have to be the most nieve person I have ever met, jobs in finance require you to be able to be numerically fluent in order to perform quantitative research. Why do you think as part of accounting and finance degrees they must do units in maths espically focusing on calculus and algebra. That because on the path to some of the highest payin jobs (i.e. investment banking and funds management) you have to be a brilliant analyst which uses calculus techniques.
grk2nv100 10 months ago
@grk2nv100 lol
roachey15 10 months ago
@gespilk these are used in physics and engineering, it aslo demonstrates an ability to do complex maths and solve complex problems. If you wanna work at mcdonalds then nah u should be fine without it :D
felixx2012 10 months ago
@gespilk
Calculus is just a tool set used to help solve problems that would be more complicated without it. Certain sciences rely strongly on calculus. If you aren't interested in getting into any of the many jobs that use it, it definitely is pretty worthless to you. I won't be using any of this for any real purpose until I start working with statistics in psychology.
Btw, a lot of textbooks give examples for how the math is used irl. (albeit over-simplified ones)
ScissorHand26 10 months ago
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BillSpike11 8 months ago
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BillSpike11 8 months ago
This has been flagged as spam show
@gespilk differential equations form the very basis of our world. So they are a fundamental part of scientific studies and are used on a daily basis by scientists, engineers, mathematicians (including bankers!). im not sure to which real life system it corresponds but the point is to practice with the simple equations. Anyhow if all you want is to look after a family,. your best bet is ta career which requires ODEs
BillSpike11 8 months ago
@gespilk Well if you wanted to work as an actuary, for example, to calculate probabilities of someone going from a healthy state to death in a certain time period, one of the steps involved requires first order differential equations. Obviously this information would be of value to an insurance company. They are useful in many other situations aswell
MrArbitrager 8 months ago
@gespilk In Electrical Engineering differential equations power every single transient analysis whether it be a program or a manual calculation.
fingerboy18 7 months ago
@gespilk
differential equation are frequently used in enigineering expecially laplace transformations
jay20112012 7 months ago
@gespilk
Agree sometimes it crossed my mind that what is the use of this equations if you dont know how to apply them in real life situations its really funny....but i guess you should pass this subject and be good to it for you to graduate :D
feelmypower2009 7 months ago
@gespilk Your obviously not an engineer (or studying to become one)
GTORIDERS 7 months ago
@gespilk 1) Almost any type of Engineer is required to know these equations from chemical to mechatronics.
2) Circuits, Engines, Reactions..
3) You'll know when you need to.
Obviously you have never heard of companies, because all companies hire engineers which are all able to solve these types of equations.
GTORIDERS 7 months ago
@gespilk Fair Comment !
topmaneldo 7 months ago
@gespilk mechanical engineering for example relies heavily on solving differential equations, as they describe the bending behavior of materials. (random example).
TekSiDoT 6 months ago
Great help man! University lecturers got nothin on you!
hymchong 1 year ago 2
Does this still work the same if you have y-or-x-squared or cubed or something like that? We had this as a topic recently and the notes were somewhat unclear...
birdsofafeather1990 1 year ago
u are a legend brotha
iamtheasianjamesbond 1 year ago
At the beginning of the video, you say to multiplty both sides by e^P(x) . . . but you seem to have meant to say to multiply both sides by e^Integral of P(x) . . .
. . . correct?
Thanks for all of your great videos. I wish you had more on Statistics.
jwmcmac 1 year ago
At a first glance it bugged me that at the first integral ( exp(integral(-2x)) ) he didn't add a constant ( c ) at the end.
After a minute i remembered that the operation of integration gives you a SET of primitives (that vary from one another by a constant), so normally he chose the primitive with c=0.
Comorasu 1 year ago
thanks for making this simple to understand
karlneumann61 1 year ago
Patrick, I was afraid of differential equations in games theory examples and now, I don't mind the kind of example because I have the rule!!
Thank you! you saved my life! :-)
joselinbogarra 1 year ago
Thanks very much for your videos. One thing puzzles me @2:15.
How do you multiply e^(-x^2) by -2xy to get [+2x{e^(-x^2)}y]
Shouldnt the product be negative?
kwakuna111 1 year ago
@kwakuna111 READ THE TEXT HE ADDS IN!!!
lol he fixed it
1upirons 1 year ago
@kwakuna111 I noticed it as well. It should be negative. With the integrating factor multiplied on both sides, the sign of p(x) does not change.
BuddyNovinski 1 year ago
dude ur awsum i missed my lec n couldnt understand a thing.....but thnks to u its on my finger tips ... hats of 2 u man ur the best...!!!
sagiterionmujtaba 1 year ago
thank you... that helped...
bigbossabhiraj 1 year ago
Great video, helped a lot. Can you make one about solving linear diff equations using substitution?
Use the closed caption option and put it on ''Translate Audio'' I got a good laugh.
abdullah57habib 1 year ago
How come you don't have to add C at 1:30?
archiemedes42 1 year ago
@archiemedes42 C is not affected by constants but is only affected by variables. In other words, it will absorb any constants. When simplified, the equation should be:
y = -[1 + Ce^(x^2)] / 2
itaffy13 1 year ago
@itaffy13 Still, at 1:30, variables are involved and he simply integrates within the exponent, and I thought a constant should pop out there because he is doing nothing more than a simple indefinite integral.
archiemedes42 1 year ago
Would the simplified answer be -1/2 + Ce^x^2 ?
Arkanovi1989 1 year ago
hey, do u have any tutorial abt the legendre LDE? i'm very much confused with all these stuffs :(
maiie5 1 year ago