Exact Differential Equations

[zoom2121]

Can you please do more examples that are relatively more complex. I appreciate all the work you have done and indeed I am very grateful. I'm sure the 93,000 people who have watched this will feel the same way :)

[MissChelsie24]

Everybody, when you graduate and have an awesome job, remember how much patrickJMT helped you through university and donate! ...or just do it now.

[BobblerBarnOwl]

Excellent, great vid!

[phanelius]

Patrick, I can't thank you enough!!! English is not my mother language, but I can perfectly understand you. You helped me pass Calc I,,II,,III,,,,,,I never bought the book because x reasons but thanks to you I'm on my way.....NOW differential of equations, Thank you!!! I've told friends about you videos, and definitively will get you some donations when I graduate :)...YOU ROCK!!!

[patrickJMT]

@phanelius happy i could help : ) thanks for telling your friends, it is appreciated!

[malibu90]

thanks sir , this is exactly the same example that my teacher solved in the class.. i couldnt ask more from you

[martmelee]

anybody could please tell me where i can find tables of integrals? my friend has this huge list with a bunch of integrals they're probably about 400 or maybe almost 500. and he won't pass me a copy. :(

[patrickJMT]

@martmelee any calculus book has them, usually at the end. you could probably just google it as well

[dkdonster]

Plz can u solve more examples for Exact D.E..!!

(x^3 + 3xy^2)dx + (3x^2 y + y^3)dy = 0

plz solv this question 4 me... sir plz plz

[McChickenn]

@dkdonster

Integrate (x^3 + 3xy^2)dx, which gives you x^4/4 + 3/2x^2y^2 + g(y), and then differentiate it with respect to y. This should give you

3x^2y + g'(y). That equation is a partial fraction with respect to y, just as the (3x^2 y + y^3)dy is; because of that you know that g'(y) is = to y^3, which means g(y) = y^4/4.

Substitute g(y) in to your x^4/4 + 3/2x^2y^2 + g(y), and you end up with

x^4/4 + 3/2x^2y^2 + y^4/4 = C

as your final answer.

Is that right Patrick xD

[dkdonster]

h(y) means x??

[roflcopter2225]

Is exact the same thing as being conservative, or is that only for vector functions?

[dkdonster]

Patric this equation is for u

(sqrt(cos(x))*cos(200 x)+sqrt(abs(x))-0.7)*(4-x*x)^0­.01, sqrt(9-x^2), -sqrt(9-x^2) from -4.5 to 4.5

copy paste it in google search...

[patrickJMT]

@dkdonster ahahahhhaha awesome : )

[halflife1994]

Do you have a video about not exact?? thnx =)

[007abhinavagarwal]

i like it

ur lvl of ques is higher than a average youtube uploader

keep it up and do some very hairy problems if u feel like doing

[jayjay71270]

Hey you're the best, maybe one day you can have a website or video! You are really great at breaking things down! Only thing is I wish I would have discover these videos earlier during my differential equations class, I'll probably be kicking butt right now lol

[bigaaal3marzooq]

c going out with minece mate



[pimpmymail]

that is TOO MUCH integrating and differentiating. Lol, like seriously TOO MUCH. Back and Forth Back and Forth....

Anyway, appreciated !!! I watch your video before i study from the book to get an idea of the thing first

Thanks :)

[crossxinfinity]

why we put solution equal to c at the end?

[PianoManX2]

if there was a constant in fx(x,y) and you integrate it would it become x or y?

[hyperice98520]

Dude... you explain in 5 minutes what my proffessor can't in a semester, I swear...

[conglacious]

What I usually do is watch a Khan lecture to get a good grasp on the "intuition" and then watch a Patrick video to solidify the process. Clear audio and great organization make your videos the cream of the internet crop.

[sharada10]

probably just saved my diff eq grade!!!!

[ToyMachine22122]

I know you're focusing on teaching the method, not practicing, but I think it would be helpful if maybe you showed a few different types of problems. I understood this video perfectly, and was excited, thinking I had this under control. But I was not able to solve the simple equation (2x-y)dx+(2y-x)dy=0 using this method; I wound up with h'(y)=2y-x^2, and now since h(y) depends on x instead of just y alone, I am lost with what to do.

Still, great video, thanks! :D

[jnolan2008]

Great explanation, could you also show some that are not so pretty? Like one that isn't already set up?

[saudisprince]

too fast .....

and please use printOut ,computer writing to made it more effective ..

[patrickJMT]

@saudisprince no thanks

[risalvat]

Really Great explanation. Thanks so much!

[godiegogo1991]

he is better than Servatius

[wpi2992]

@godiegogo1991 anything is better than servatius

[LoveRockMe85]

Nice 1

[BoredAlways]

Holy shit, why aren't you a Nobel Peace Prize winner?

[XBLAQPHYREX]

Thanks much. This beats trying to understand it from the textbook by a long shot! (I hate math textbooks this is so much easier to understand)

[kazmanX]

Just sent you a small donation. i'm a broke college kid but i hope you continue with what you are doing and maybe one day i will be able to help out people too just like you

[patrickJMT]

@kazmanX super duper appreciated. if i got $.05 per view, i would be a super happy guy : )

[JaktheAtheist]

@patrickJMT

and a millionaire

[patrickJMT]

@JaktheAtheist this is true!

[southpawking1]

What I really like about these videos is that the technique is shown really well. When I ever I am learning something new I always place emphasise on the technique and its done really well here.

[Cammie010]

nice video, I think you should give an example where My =/ Nx to highlight what happens if the conditions are not met

[Karestasse]

@Cammie010 THATS A HUGE BITCH!!!

[Pianoblacks]

Who in the world dislike this video? It CAN"T BE ANY CLEARER!!!

[MrPve123]

thank you so much sir!

[MakenX5]

Thanks so much man, you are a true pimp!

[plastefuchs666]

It amazes me how you are able to write with your left hand on a dry erase board. I always struggle with that, even the old chalk boards gave me trouble.

That is why i hated to get called before the class and write something on the board. <.<

[sundaricoolgirl]

super like :) it was really helpful :) \o/

[fingerboy18]

I want to solve (e^(3x)sin(3y)+(1/(x^2-4x-5)))­dx + (e^(3x)cos(3y)+e^(4y))dy = 0

Is there a way to check my work? Wolfram Alpha times out and I'm not sure how to use the TI-89 to check.

I got (e^(3x)sin(3y))/3 - (ln[(x+1)/(x-5)])/6 + (e^(4y))/4 = C

I found My and Nx. They are equal, which means it is an exact equation. Then I simply followed the process.

[doctorsanch]

u should try to get an endorsement from the markers or whiteboard company. that would b beast

[TheGarr123]

Good video....... this is the first time Im coming accross this type of differential equation and you just explained it amazingly... cheers

[carloznds1988]

great men!!!, you was a lot help for me..

greetings from colombia

[hyracatherium]

I was doing this along with you and just realised, not only are the videos amazing, We use the same markers.

[92310CAMILLE]

amazing ,thank you a lot

[tucense]

In my book there is a dx after the M and a dy after the N.. you have y' notation. its just a little bit confusing.

[ziadarwady]

Thank you so much

greetings from Cairo - Egypt ;)

[gopio9]

i know this doesnt really matter but where you see y prime i think you should of explained how that relates to the first order diffferential equations general form just saying even though it doesnt change the answer or solution

[Blitzcrag18]

thank you you are amazing

[MKL131366]

Thank you so much for your help Patrick, because of you I am going to pass differential equations

Take care yourself and keep posting videos you are awesome dude¡¡¡

[pohdohloh]

love ur handwriting...neat and small so u can fit in lots of stuff on a page unlike mine...gr8 job!

[000jawad]

u rock.... :P i passed my calculus paper evn still m learning frm ur vids :P ... best teacher ...*thumbs up*

[CGRLW]

how would you differentiate: y' = 5t - 3(y^.5) y(0)=2 i cant seem to figure out what to do with the radical y

[twirmd]

@CGRLW

Bring them over to the left side:

(3*y^.5 - 5t) + y' = 0

M = (3*y^.5 - 5t); N = 1

My = (3/2)*y^(-1/2) ; Nx = 0

Since they're not equal you have to use an integrating factor. Khan Academy has a couple good videos on how to solve using an integrating factor. Another place you can look is sosmath(dot)com. Go to the differentiable equations section and read the section 'Integrating Factor Technique'.

[CGRLW]

@twirmd thanks alot, what about an ode where both M w.r.t. y and N w.r.t x are both 0? does it mean they are exact or they arent allow to equal zero?

[twirmd]

@CGRLW Sorry for the really late reply. I didn't see your question in my inbox until just now. If M.y and N.x are both zero then they're still exact.

[Zadamanim]

im just noticing I've seen hours of this guy's videos and all i know about what he looks like is the back of his left hand...

[patrickJMT]

@Zadamanim that is just how i want it.

i tutored two girls for about a year before they realized they had been watching my videos. : )

one day, one of the girls was like: you sound just like this guy on the internet whose videos i watch. you even have the same name...

[TeshiKennedy117]

@patrickJMT so you're not the guy in the background image of your channel?

[lazarpandar]

@patrickJMT

Did you fuck said girls?

[mkinsel19]

Excellent once again, Mr. Patrick. Could you possibly make a video showing the process for using an integrating factor to "make" functions exact when M'(y) does not equal N'(x) in the original function? It's confusing the heck out of me, and I know you'd be able to explain it simpler than my prof....

[brco2003]

Khan Academy did this exact same example, but this was much neater.

[patrickJMT]

@brco2003 where is my $2,000,000 grant ? : )

[brco2003]

@patrickJMT LOL. Pat, you have heart and soul and that's all that matters. (Also, Khan has a large and diverse library and an educational vision.)

[patrickJMT]

@brco2003 he is doing great stuff and deserves every penny. i was only joking (although some have taken the comment a bit more seriously for whatever reason!)

[rajneeshdewan]

@patrickJMT I was going through Khan's tutorial for exact equation. But after I found your's, it really helped me where I got stuck with Khan's. You are really gr8. you also deserve every penny because you are damn good in what you do.

[twirmd]

@patrickJMT I wish Khan Academy would expand out more and bring in a few more tutors, including you, for video leactures. You're on par with Sal and your videos are easier to read (no mspaint!).

[ironicRON]

what does the (x,y) mean?

[321boileranimal]

Your video kicks the Instructor from MIT in his Pussy. 

[patrickJMT]

@321boileranimal karate *KICK*

[mariomaruf]

@321boileranimal MIT lectures and classes are difficult for nearly everyone, even the students who go there, partly due to the fact that they also develop intuition and not just how to do something. Patrick teaches you how to identify and solve these equations and sort of develops algebra and calculus skills through his many many examples, but goes over it so briefly that it best serves as a review before an exam and a tool to clear common confusion.

[321boileranimal]

@mariomaruf With my Calc book, I felt that going to class, mostly in Calculus two; was a waste of time. because its so much easier to read the theorems do the problems, then ask questions later for 20 mins. and move on. However in my Diff EQ book, the examples and theorems are not written as fluently, or articulately , the therms are much harder to follow rather then being broken down like in the Algebra books and Calc books. Where there are many colorful examples.

Cheers!

[mariomaruf]

@321boileranimal Is your book published by Dover? Those books are pretty hardcore compared to high school books, and while you could definitely learn Algebra and Calculus in a month with the books used in high school, 2nd year level math is a more full level of math which is usually taught in a completely "Theory --> Problem --> Repeat" sort of way that translates directly to most popular books including the cheap Dover line. I guess Patrick does well to get rid of that overly general fluff.

[mariomaruf]

@321boileranimal He could easily be more intuitive but many people don't like that approach very much because the whys and theories behind things clutter understanding and can easily heighten one's confusion. I get really confused by those lectures too but the reason I understand them is because I use some additional supplements like a book or Patrick's videos, just to narrow down the absolutely necessary information or to set up the frame before I put in the picture..

[ohhitsloveee]

@321boileranimal

Same with my calc teacher at UPenn

[sbsaad]

even though its hard , but you made it so easy !!

to HELL with my teacher!!

[patrickJMT]

@sbsaad well, that may be a bit harsh : )

[yyourfacee]

why does it seem so complicated in the class notes and textbooks :(

[Zadamanim]

@yyourfacee because they're getting paid

[Zadamanim]

@yyourfacee because they're getting paid regardless of if you learn it or not

[mclawson232]

It doesn't look like your video has been praised in over a month so I believe it is once again over due... If you do not already have a lucrative teaching job you should...

Very well done sir

[n0pr7]

THANK YOU!!!

[marquelmah]

your steps are simple and clear, thanks a lot

[Chris910817]

Your teaching is clear and awesome. I learnt from you more than all my maths lecturer. Thank you so much!!!

[walcXP]

Just five minutes to completely explain a thing that I've been struggling to understand from my lecture notes for the past 20 minutes.

Great thanks!

[garnacov]

You speak another language than me and you're clearer than my teachers. Thank you so much for the vids.

[patrickJMT]

@garnacov ha, happy to help : )

[wo0725]

amazing~you save me!!!

[sweatpants1212]

dude, you got what i need

[Bmsscott]

did you miss the x' for the ycos(x) + 2xe^y . Should the question be (ycos(x)+sxe^y) x' ....ect

[linkinwayne]

Brilliant. 

[maksingh10]

undoubtedly the best teacher ever.

[jakbruce2008]

feels like I just came out of an hour of Diff EQ class, except I know what you were saying XD. This should make homework much easier.

[MistryWho]

Oh my god. Thank you.

from this one vid i've seen, you already make up for me not having the textbook and a lousy Prof

[farshadguitar]

Patrick = Chuck Norris !

[aaaraura]

Thank you so much. I can't believe a 6 minute youtube video cleared up confusion from an hour class and 2 hours of reading the textbook.

[Crunchysann]

Dude, thank you sooo much. I spent five hours trying to figure out what to do after finding out that the equation is exact. Great presentation.

[nicholaschase29]

Can you explain why when you do the partial derivative of M and N you take the derivative with respect to X on the M equation and the derivative with respect to Y to the N equation. I don't see this algebraically. It makes sense to me when the equation were written as (M)dx + (N)dy) = 0 but here it's (M)+(N) Y' = 0 and I don't see how you get there algebraically. Thanks.

[MrRendellious]

@nicholaschase29 (M)+(N) Y' = (M)+(Y) dx/dy yes? Then multiplying by dy gives you (M) dy + (N) dx

[wshark931]

I have recommended you many times to my friends, I guess why professors aren't called teachers is because they cant teach! You are a saint in the world of mathematics, possibly a god.

[patrickJMT]

@wshark931 glad u think enough of the vids to recommend them to others : )

[bunny188]

THANK YOU!!

[Electrickl]

Thank you

[uchihaitachi33023]

if our derivative of the arbitrary constant is found to be equal to zero does that mean our constant is simply c and that our f(x,y) is therefore just the integral without the h(y) equal to a constant?

[tosyn33]

I spent half a day trying to understand this on my own.

God bless u.

[patrickJMT]

@tosyn33 glad the vid helped : )

[cobster123]

@patrickJMT Dude your awesome at teaching, just wondering what qualifications do you have and what grades did you get in maths ? thanks

[djdoom99]

you are the best sir. thank you so much ;)

[2821sunny]

it is very helpfull........

[styleguru1986]

hi,

I first of all thank you for ur great help .

I have a question and i need its solution  plz help me , the question is

y=(1+p)x +p^2 ; where p=y'

Thanks alot

[calculus89]

@styleguru1986 Do your own homework.

[ravi2253]

Thanks a lot! That was fantastic

[ar81rome]

spent an hr reading a text book and cud not understand ...........looked at your video twice and i got it...YAY!!!!!!!!!!11

[tonyw1988]

I have the exact same problem as an example in my book, but patrickJMT just explains it WAY more efficiently and is a lot easier to understand. THANKS!!!

[BoobsVsBoobs]

bad volume voice

[SuBliMe420zzz]

I love you.

[AreThereSexy]

i have 1 question :

patrick why while u do derivative u did not use product role . i mean N , M

[dramajoe]

@AreThereSexy

They're partial derivatives. That means that you take the derivative with respect to a chosen variable while treating the other variable as a constant.

[loly717]

i think the equation is like that

h ̀(y)=-1

h(y)=-y+c

f(x,y)=y sinx+x^2 e^y-y+c

[Gleeful90]

@loly717

Just set that equation equal to zero and move the c over, you'll get the same equation as him. :)

[khalid97899789]

where is non exact examples my teacher?

[JVinci16]

this is the by the book way. when you find out they're exact, you'll see that you can actually integrate them and piece them together straight down without all that variable crap. that gets confusing.

[cfl941]

thx man, trying to read that out of the book was a pain in the ass

[tennisIS4pussys]

amazing

[comaster07]

at 3:18 isnt its supposed to be -ysinx cuz the derivative of cos is -sin

[IanFarias00]

On this step he is integrating the function, not derivating.

[scott01019]

he didn't take a derivative he integrated.

[genomstic]

no he was integrating there

anti derivative of cos x is sin x

[555DarkLord555]

@comaster07 he is integrating with respect to x so its positive sin.

[lifematch]

what if it's not exact. is there anyway you could make it exact?

[theonlyrealshark]

sometimes you can with an integrating factor-

[IanFarias00]

Watch Khan Academy videos, most precisely the "Integrating Factors" ones. It tells you to multiply the whole first equation by an especific function.

[genomstic]

you could possibly mess around with trig identities if its sin and cos

[tennisIS4pussys]

@lifematch yes, I cannot remember how to right now, but in some instances you can make it exact

[jomomaisamofo]

you find the integrating factor

[MrMasonMMA]

would of know about these i would of never of dropped cal 2. well... maybe i would have anyway, who wants to learn cal 2 at 7 am. hehe

[brco2003]

Are you using the textbook by Boyce?

[me2kool4u]

Great Video man! It helped me out alot!!

[lickachair4fun]

i "glazed"

[cochisewolf]

No fan fare or fluff, precise, to the point, very clear in the presentation. In short, an excellent piece of work.

Thanks for posting this and I'll be checking out the rest of your videos and website as well.

Five Stars.

[musesparrow]

You're a legend for posting all of these videos up!

[3lGranGon]

Thanks for this JMT.

[PostalTubeAlex]

fellow left hander! haha.

[97360401]

THANKS

[axelasdf]

What is the backwards "E" symbol in the start?

[jishuenkam]

it means 'there exists'

[electricsashimi]

YOU SAVED MY LIFE!

[jamesqwerty87]

I understand the steps that were taken, but why is the final answer equal to C? I don't see how the final answer would be a solution to the initial problem.

[ikarusbodom]

because f(x,y)=K, where K is iqual to any Constant and thats why is a "C". in other words, thats by definition and in your exams try to put it like that because even though you have solved it properly, but if you dont put it like F(x, y)=C or K, its a bad answers.

my opinion: its just an extra step. but do it.

[GMFroggy]

can you make a video on how to find gradient of curves?

[kipman725]

Hi I found this video usefull but you need to improve the naming of your functions! if you think about what you are doing you are calling two distinct functions both f(x).

[Foaman]

So.... what if it's not exact?

[SquarangularPrism]

use another method

[daverandomster]

If it isn't exact you should try to find an integrating factor that makes it work...but I'm not sure how to do that lol

[cwxzeng]

If not exact, u may use the method of Seperation or use integration factor.

[faheemafr]

please i need ur email

[abarrien00]

great, i missed class today and have a quiz tomorrow, you just saved my life for this section! hooray!

[assblood1]

awesome

[adhikarisubash]

Thanks Patrick! Finally, I understand and can solve exact differntial equations!

[eznamee]

Forgive me but, are you missing a dx in the first function?

[DRCE777]

u mean dx or x' on (ycosx+2xe^y) ?

[1950slollipop]

My and Nx are equal to 0 is the equations still exact?

[bigheadbang]

bodoh....

[bigheadbang]

left handed people can either mean they're smart OR goodlooking. either one of both. la la la

[patrickJMT]

i dont think i am either... so too bad for me

[patrickJMT]

i bet you are both though

[crownhellfire]

thanks..

[dunesandcoons]

yup