Solving Separable First Order Differential Equations - Ex 1

[TubHmoobVwj]

At 4:32, you said let "E=A to the C" but wrote "A = E to the C". I've become good at paying attention to detail through your videos. Thank you!

[bossbower]

Do you think you can do a video on Ricatti equations?

[illisanantexico]

I thought the e^(½ ln |x² + 1| would reduce to simply (x² + 1)^½ since e^lnu = u.

***(I am not doubting you or trying to call you out. Just genuinely curious for future reference.)

[patrickJMT]

@illisanantexico no you are absolutely correct; i thought i had annotations pointing out my mistake.... * goes to check *

[patrickJMT]

@illisanantexico yes, it is there :)

[illisanantexico]

@patrickJMT my apologies, Sir... Again, I in no way would intend to undermine you or anyone else for that matter. I often second (and third) guess myself... Often to a fault. Which is why I'm watching you videos. I have learned a lot from you and would like to return the favor someday. Thanks again! :o)

[patrickJMT]

@illisanantexico no need at all apologize :) some of the videos do have mistakes and someone needs to point them out! feel free to comment any time

[kmrobir]

At 1:20 why don't the y's cancel out? 

[kmrobir]

there is 1/y dy on the left hand side...

[bobbbyyy1]

a very useful example. thanks

[ChrisTheDIYguy]

you're a lefty! me too!

[MattyHild]

How can you just tack on an integration symbol without adding a d*(star being whatever variable you're integrating with regards to)?

[rosjio99]

Hey Patrick, when you use the natural log rule and bring the coefficient inside the term on the right. Is it still being exponentiated?

[MrBosox92]

when u take e to the power of the right hand side doesnt the ln on the right side go away? i got answer of y=A((x^2)+1)^1/2

[vinvinnabulation]

You have the best handwriting for a math teacher. I have a very big mancrush on you. Thank you for all your help!

[patrickJMT]

@vinvinnabulation you are welcome. nice picture

[logator]

Homogeneous first order ??

[tdr124]

I am confused about the left hand part. Why after you integrate is there no constant, but there is one on the right?

[jmmtcidc]

@tdr124 Technically there is a constant on both sides, but they can be combined to form a new constant which you then solve for.

[MangoClownfish]

@tdr124 see @MrBosox92, but re: your question, you're right, there is a constant on both sides. Call the left constant D and the right constant E. Now subtract D from both sides. Now let C = E-D. They're the same thing. Where you're lost, I think, is in the language. C doesn't mean "plus some special constant you need to find," rather, "plus any constant the specific boundary conditions of a problem might require." It's actually a set of solutions. Hope that helps.

[iwasanil]

you are my saviour

[baker11108]

Your videos rock! I'm taking an ETS Major Field Test in math tomorrow...too much info to review over 4 years! LOL.

[MHarlom]

Has someone mentioned you rock?

[TheExtractor1]

Thank you very much! Love your videos.

[JohannVF]

You're much, much better than the DE instructors at the University I attended.

[skatty14]

OMG, I wish you were a physicist and and a chemist too, then I wouldn't have to feel so stupid in those classes either! ;)

[sha31337]

Please make one video one first order homogenous equation, there is none :(

[nbernabejr]

do you have a video where the equation is not exact and you have to find an integrating factor?

[HeavySpinna415]

Nice video. Are u a engineer lol?

[patrickJMT]

@HeavySpinna415 rocket scientist

[dojOdRiFTeR]

@patrickJMT u r a god godddddddddddddddddddddddddddd­dddddddddddddddddd

[patrickJMT]

@dojOdRiFTeR that is the last thing i want to be! just a normal guy here, doing what he can.

[dojOdRiFTeR]

@patrickJMT too late mr math goddddddddddddddddddddd

[ParkourNerd]

@patrickJMT God complex fun!

[Monosaccaride]

@patrickJMT

OBAMA vs OSAMA rap battle XD!~ plsss

do it.

[aMammoth]

@patrickJMT Propulsion Engineer?

[metalman134]

So the answer should be y=A*sqrt(x^2+1)?

[metalman134]

Isnt the natural log canceled out since its been eponentialed"

[fearlescatcher]

You made a mistake. When you exponentiate both sides you eliminate both natural logs. you left one

[patrickJMT]

@fearlescatcher i know, as the annotations point out, i guess no one bothers to read them : )

[Seanpitcher007]

@patrickJMT Nah, we see it. The concept of seperable D.E.s was conveyed even if the algebra was off. Glad for the evidence of humanity.

[Seanpitcher007]

@patrickJMT Nah, we see it. The concept of seperable D.E.s was conveyed even if the algebra was off. Glad for the evidence of humanity.

[assbelonker279]

@patrickJMT lol, i like the little sarcastic smile. u have personality.. for a while i thought u were a robot with human hands.. but honestly thanks for all the video's, because of u, i feel like i'm wasting thousands of dollars on classes that i can just take on youtube.. n also cuz i've passed calc 1 and 2 so far cuz of u, so much props, i hope that things go well for u cuz u've helped me so much now n probably in the future n i can't thank u enough

[Jozekban]

water fire air and dirt. fucking differentials, how do they work ?

[GuitarPeeker64]

NIce teachings... but still I need to review my calculus

[weatherallc05]

have to praise you for your teachings, cos i woldnt have the nerve to teach a topic which features at the end of a level , and features constantly in further maths. takes some nerve, and u ahve got that nerve

[PCH456469871278]

little more complicated?

[boala2]

I know this is a linear one but still!! Theres a question that i am having bother applying this method to:

y' + y = 1 / (1+e^2x)

Any help would be greatly appreciated!!!

[ranile1]

help! what can calculus help us in real life? i mean algebra can definitely help us, trigonometry can help us, solid mensuration can help us, but what about calculus?

[kadleck69]

@ranile1 Engineering

[GuitarPeeker64]

@ranile1 Nice question man... Algebra, Trigonometry, and Solid Mensuration are all applicable in the community... Calculus... although a complicated and head banging branch of Mathematics, has a application in reality. Like Differential Calculus- you can solve how much cement is used to create a good building (maxima and minima--> the higher the input, lower the output). Integral Calculus- useful for getting the area of a measured land. I know it's still complicated but try to think of it...

[wqrahdful]

u r the best patrick.......but can u help me in fourier plz...plz upload videos on fourier series...plzzzzzzzzz.....

[Username93611]

Out of curiosity, do you use noise reduction on your recorded audio? It has that very warbly underwater sound that I hear when I've been too overzealous cleaning up some analog to digital transfers.

[patrickJMT]

@Username93611 i have used a bunch of different mics - not too happy with any of them. i think i need some anti-aliasing on the new ones

[Username93611]

@patrickJMT

Hmm. One suggestion. I don't know how much you've spent or what you have for more recent videos, but, silly as it may seem, the original Rock Band microphones are actually quite decent. You have to cut the cord behind the logitech ADC USB unit (it's terrible quality and has tons of noise reduction) and solder to an 1/8th inch jack so it's the pure analog signal, but it's quite decent and cheap.

It's not a particularly flat response, but a one-time EQ would fix that.

[patrickJMT]

@Username93611 thanks for the suggestion! i am going to try and get it sorted out soon

[theguyi26]

@patrickJMT It sounds like your mic sounds okay; the problem is that the audio is being processed after it is recorded, probably heavily compressed in mp3-format or something.

[theguyi26]

@Username93611 What you heard originally was correct. There's some sort of "processing" like mp3 compression or noise-reduction (they both sound very similar).

The mic has nothing to do with the problem.

[Username93611]

@theguyi26

I don't know that mp3 compression sounds similar to noise-reduction at all... in fact I know it doesn't, but what do you mean "the mic has nothing to do with the problem."? What mic? Which problem?

[theguyi26]

@theguyi26 You mentioned an "underwater warbly sound". That is what I mean by "the problem". This kind of problem as far as I know cannot be caused by microphone quality.

As for whether or not mp3 compression and noise reduction sound similar, it is my opinion that mp3 compression, noise reduction, and Satellite radio (XM) all give the sound a "similar" effect i.e. "underwater/warbly". Of course you may have more sensitive ears and have a more strict definition of what "similar" means.

[InfectedMelody11]

Hi Patrick!

on the Left side of the equation we are left with Abs(y). If we are solving for y, should we worry about the absolute value ??

Could we write the final answer like this

y= + - Sqrt(x^2+1).A

replacing + and - on the right side, for the absolute value on the left side???

I thank you very much for time and your outstanding videos!

[Conflictzor]

Patrick I am really confused with this DE.

y'=3x^2(1+y^2).

It looks like a Riccati but im not given a partial solution.I solved this as separable but it looks like extreme easy :/

[Gytax0]

Where can I find the basics of differentials? I'm so green at this.

[NawMeegn]

do you also know the meaning of life? cuz you seem like a super smart guy.

If I could meet one person on youtube, it'd probably be you.

Great video and thanks so much for taking the time to make such useful videos.

[patrickJMT]

@NawMeegn ha, i am very flattered. hopefully i would not disappoint you too much in real life.

[Rizmaestro]

Cheers!

[saudimiker]

Should the natural log still be there on the RHS? Why didn't it go away when you raised to the e power or whatever?

[patrickJMT]

@saudimiker yes, it should be gone; i made a mistake in this one. i added annotations to point that out.

[fazekaslaszlo]

Thank you, great work again!

[jmetalhead]

Hi sir, do not understand how you integrated the RHS at the 3rd step.

why do u have a 1/2 term?

thank you.

[inuyasha103190]

Can you take out the absolute value from y and make the right side the + or - ?

[frivoulous11]

@inuyasha103190 Yes, and then A would turn into C which is all real numbers besides 0 or (+ or - e^c)

[blackyurizan]

I have no idea whats going on

[patrickJMT]

@blackyurizan about this problem, or about math, or about life in general. cause if you are talking about life in general, i am with you on that.

[opmike343]

@blackyurizan

I'm talking this class this semester, and I feel the same way during every lecture.

[juhijaferii]

@patric: do you know how to integrate e^(x^2)

[patrickJMT]

@juhijaferii yes

[juhijaferii]

@patrickJMT How?

[divinitiescreature]

@juhijaferii let u=x^2 and solve by substitution

[patrickJMT]

@juhijaferii it does not have an elementary antiderivative. you have to use a taylor series expansion.

[mpatt79]

let e = A^c lol.....we know what you meant

[18Zac1992]

Thanks a trillion!! Your explanations make heaps of sense! They clear up my confused brain about easy things lecturers tend to enjoy complicating! :P

[FrauLahnstein]

It is actuayll not clear why one is allowed to multiply both sides with "dx".

More concretely: "dx" is not a variable. So this requires more explanation.

[patrickJMT]

@FrauLahnstein well, these are supplements and not meant to be a 'stand alone' lecture on the topic. any text book on the matter should explain it.

[FrauLahnstein]

@patrickJMT : Thanks for your quick reply! You're right it should not meant to be a 'stand alone' lecture - however, I have never come across a text book which actually explains it! I would be grateful if you could give a reference where the multiplication of dx is justified (or at least heuristically explained).

[BatchiK67]

@FrauLahnstein

dy/dx is change in y over change in x. so you can multiply a change in x by both sides to have change in y on one side and change in x on the other.

[BatchiK67]

@FrauLahnstein

dy/dx is change in y over change in x. so you can multiply a change in x by both sides to have change in y on one side and change in x on the other.

[777decent]

Thanks a lot for your crystal clear explanations.

[ermitz90]

I wish to see the next example on this subtopic...thanks Patrick.

[obusom37]

Boss

[khalid97899789]

constant is another term not take in term of ln (√(x²+1))...

right answer is √(x²+1)) + e^c

[Cybernetic]

where is EX 2?

[shapurII]

Hey make some videos on Orthogonal Trajectories and Mixing Problems from the Separable Equations section in the Calc. book... Thx :)

[mitchyc2012]

Besides the already discussed mistake. Wouldn't the final e^c value be ADDED to the result instead of multiplied? so abs(y) = sqrt(x^2+1) + e^c Therefore, abs(y) = sqrt(x^2+1) + A

[kathysoiio]

@mitchyc2012 you have to remember the rule that says: [X^(a+b)]=(X^a)(X^b)

[jaibhambra]

in the first example you don't have to use integration by substitution. You can multiply by 2. This way the x function will be 2x/x^2 + 1. Since the differential of the denominator is equal to the numerator it integrates to the natural logarithm of the denominator. Just a quicker way if you want to save some time.

[kiat1871]

can you show how to solve

dx/dy=(x+Y^3)/y

[kevinpotts1]

I think it would be nice to mention also that when you get 1/y you assume y to not be 0; but the final solution could include 0. It needs to be understood that as soon as you have a y in the denominator you need to make a not and go back to see if 0 is a possible solution.

[fttank]

PatrickJMT my friends and I always have study dates with you on youtube :P

[xjimmy10x]

lmao I coined the term "i have a date with patrick jmt"

[alistan91]

Patrick you are a very good teacher ur helping alot through calc 2 =)

[Frank12387]

Thank you Patrick. You're the man!

[Frank12387]

HEY PATRICK, i think u made a mistake in this video... shouldn't the final equation be |y| = A(√(x²+1))... i thought "e" to the power of "ln" they should cancel out each other, so i think you forgot to remove the "ln" from the final equation...

[patrickJMT]

you are right. there is a text annotation pointing out the mistake though already

[scarykidbryan]

@patrickJMT yeah I think Frank had his annotations turned off or something

[heyyhowyadoin]

lol. but nice try  n e way frank.

[alphacat626]

does anyone know how to integrate something like (x^2)/dx, where dx is the denominator? thanks

[lenorag88]

can u move them to the other side of the equation? so u will get dx/x^2 at the other side..

[jsteh22]

thanks man your amazing. PLEASE make more differential equation videos. your videos are the only reason why i got through calc 1 and 2.

[friederich89]

thanks mann,i feel ya help :)

[Moonbladez123]

thnx for the idea.....

[3lGranGon]

This is win!

[ghassanmas]

great

[lickachair4fun]

nice this question was one of my hw questions

[draganegoelme]

Thank you so much!!

Really appreciate it!

[69shepsie69]

after u raised above the e power, why did u keep the natural log of square root. should the Ln not be in the final answer

[rbhoera]

i thought the same...

[rbhoera]

I thought the same...

[kashiark]

Why didn't the absolute value bars carry over?

[ExecutorIves]

because it will never be negative, X^2 + 1 already took care of that.

[kashiark]

Ah yes, I see; thanks!

[wizardroolz]

hmm..

wat abt boundary and intial conditions?

[eackpal]

patrick...you rock my world!!

[blackhotboy242]

Thanks this helped tremendously

[luisrodriguez88]

Patrick, I cannot begin to THANK YOU enough for all your help through all your videos.. you are simply amazing!!!! Most (if not all) teachers in USF are foreign and have a THICK accent: making the subject impossible to digest. I promise you, that whenever i become an engineer, you will receive a donation for your services lol :) again.. thank you

[edzbaddest]

it really sucks ur lefthanded cause you manage to cover all the work when pointing at it

[patrickJMT]

you cant win 'em all.

i have another video where i reverse the image, so it looks like i use my right hand. would that help?

[edzbaddest]

i'm sorry i was being bitter because i had a final today...thank you for your help

[patrickJMT]

only a test, do not let it get you down : )

[aztips]

X-D Hilarious!!

[markuseraccount]

@patrickJMT what do you mean only a test..like a final doesnt have a big effect on your gpa..if everyone had that mentality everyone would fail out.

[bronze83]

@markuseraccount "it's only a test" as in don't let it consume you. Anxiety is not synonymous with preparation. If you fail, learn from your mistakes and try again until you succeed. If you place so much emphasis on it you might quit trying if you don't get a desired result.

[markuseraccount]

@bronze83 I understand but if you take a test serious then most of the time anxiety comes with it. I can tell you that if I didn't have the anxiety of a test it would not scare me into studying or practicing my material as much as I do now.

[kingofgimp]

@patrickJMT .lol....good one, haters gonna hate tho. great vids as always

[zk3991]

Thanks a lot! This video helped so much, great review video before my exam.

[drummerboy0777]

Thanks man this stuff helps alot

[pitdgret2]

I been watching your videos since differential calculus until D. E. you have a very helpful videos sir....keep it up ^^

[Guitarman8905]

Thank you so much. I'm reviewing for the Calculus BC exam in May and your videos are extremely helpful.

[humbertogarza86]

It looks like you forgot to cancel the ln and e on the first term. Check it out further.

[patrickJMT]

i added text annotations pointing this out.. perhaps u missed them.

thanks though

[futbol324]

This was great! I was shaky on it, but came away understanding it real well. Keep it up, and thanks!

[joesquills]

Let A=plus or minus e^c so you can solve for y rather than lyl

[drewski5000]

Holy crap! I have some freakin hella crazy teacher who isn't helping at all and you come in with a 5 min snippit and explain that whole thing to me NP. LOVE! please continue!

[angry4nus]

hey that's #3 in my book!! haha

[mitmfan]

Wouldn't the answer not contain ln. You have 1/2 * ln(x^2 + 1) + C, and exponentiate it to obtain e^(1/2 * ln(x^2 + 1) + C), which equals e^((ln(x^2 + 1)^(1/2)) + C), which equals (x^2 + 1)^(1/2) * e^C. In other words, the ln is canceled out by the e, since they are inverses.

[patrickJMT]

ops yes u are right!

i tried to do too much at once!

thanks for pointing out my mistake!!

[patrickJMT]

i added annotations pointing out my mistake and gave you credit!

thanks again!

[Prey2Hunter]

I taught myself how to solve most differential equations when I was 14. I got up to the nth-order linear nonhomogeneous differential equations with variable coefficients but never really went into the hypergeometric series.

[rimon890816]

Yeah sure boyo, And I am superman

[patrickJMT]

howdy! if you have any meaningful comments about the videos, please leave them here! stupid comments will be deleted : )

[jayprettyman]

I love your videos you are literally the sole reason I got through calc 2. You are 10 times better than any math professor Ive ever had because you speak casually in a way that normal people can understand. I just started diff eq and it would be awesome if you could put up some more videos ASAP!

Thanks again!

[patrickJMT]

glad the vids helped out with calc 2! i may put some more DE problems up soon. i have another crazy busy week though! : )