ODE | Linear versus nonlinear

Examples and explanations for a course in ordinary differential equations.
ODE playlist: • Ordinary Differential ...
In this video we explain what a linear differential equation looks like, and give some examples of nonlinear differential equations. This is done by analogy with linear and nonlinear algebraic equations. We give the general form for a first order and a second order linear differential equation.

[@jossell911]

3 mins compared to an hour and 25 mins in college. This guy is amazing!! Thank you!

[@olly311]

jossell911 Literally, it's so straightforward I don't get how this takes so long in a lecture and it's still not really clear

[@planetz-976]

I know right! This guy explained it better to me in 3 minutes then my professor did in an hour lecture.

[@michaelanonymous7492]

I hate my class I waste time there and the professor is trash

[@mirandamartinez569]

my d.e. professor is the head of the math department and yet this guy still knew how to explain it better them him....

[@penguinstalker1238]

Hahah I'm learning this in grade nine

[@AntAKillaButDntPshMe]

Thanks for your explanation. It helped me an awful lot. Keep up the good work friend.

[@melai21]

thanks!! this helped a lot:) and yea last one is linear

[@Alexandermajor]

What specifically make an differential equation linear and non linear is it the exponent or because your multiplying y' with the dependant variable

[@maryamyasser1643]

🙂❤️

[@completelystupid87]

last one is the 1st order linear differential equation

[@arunag3885]

And non homogenous

[@bryanfuentes1452]

Yeah, First Order Linear Non-Homogeneous Ordinary Differential Equation with Non-Constant Coefficients.

[@muhammetfurkan6818]

and non-autonomous :D

[@tempestandacomputer6951]

nerd

[@angelicdreamer2257]

@@tempestandacomputer6951 lmaaaaaaaaao

[@markymark443]

Correct me if I'm wrong, I think the last one is linear because it follows that form a(x)*y' + b(x)*y = c(x) where a(x) = 1, b(x) = x^2, c(x) = sin(x). None of the terms with y or a derivative of y have an exponent or sin or cos or log or anything so it is linear.

[@thomaszinkkoelle5453]

You are correct sir!

[@YairCat]

Nice from the future

[@WafflesToTheMax]

Nice! Great answer

[@rocketgirl86]

This!! the most simplest explanation! I finally understood with just your two sentence comment lol Thank you!!

[@ozgurertenoglu]

YESSIR

[@mokarrommolla5820]

"That's some crazy thing" lol

[@gwa1654]

The last one is a first order linear differential equation

[@martinkinyanjui7237]

Exaactly..

[@YoLo-zn4bi]

I can't believe how people can make this kind of video! Awesome and I am appreciate your work

[@giannacox621]

Thank you for taking the time to explain this in plain english and provide examples for comparison. Very effective way to teach this. You rock!

[@luvrajkhadkabk8715]

3:15 why did he say double prime when it is single prime? Also are you sure its non-linear?

[@MegaMaxclan]

I have the same doubt!!

[@makasa34]

Great video. Easily clears up my confusion. Thanks! The last one is a first order linear equation

[@neelmodi5791]

I suppose that the last one is linear then

[@markymark443]

Correct. It follows that form a(x)*y' + b(x)*y = c(x)

[@eismael22]

First off thanks for the video, it helped to understand a lot better. I do have a question about the last one. And for y'+x^2y=sinx, why is it linear? I thought two variable mutliplying each other makes it non linear?

[@gabrielleshull3246]

+Erich Plate That's the case for algebraic equations, but for differential equations it is linear if all of the terms with the function and its derivatives in them are in the form termn(y(x),x)=g(x)d^ny/dx^n. So you can see why that last one is linear.

[@1800notarealnumber]

fucking thank you, for fucks sake why did it take me so long to find a clear concise explanation of this, its usually just a load of videos that throw the standard form on the screen and go “get it?” but then are somehow an hour long. fuck. good video, thank you

[@TheDua86]

it is linear Diff. Equation, is it ??

[@jovanking42]

Yes 😭

[@Vonzi0000]

3:20 It's a first order linear non-homogeneous ordinary differential equation. So it's linear.

[@jenniferchew5663]

Thank you so much! You seem to have a real gift for explaining concepts, and so many people, like myself, are benefiting from it. Very helpful. :)

[@Latripleline]

Out of topic here but what makes y1y2 = 1 a hyperbola ? Theres neither y^2 nor x^2 in that equation how did you find out?

[@treychesser9273]

SAME hah

[@claremcdermott8396]

Just to clarify.. is a linear ODE where the dependent variable appears in a linear fashion?

[@poompongjanchei4296]

Bro conclude what my professor said in 1.5 hours in 3 min.

[@kumarannk751]

First order linear and non homogeneous eq is answer for last one🙂

[@michaelanonymous7492]

We should all just watch youtube videos in class

[@Ultisymo]

2:10 Haha couldn't have said it better myself

[@abhishekgujjar9078]

is x^3 (Y2)^2+x (Y1)^4=0 a linear equation or a nonlinear equation??????

[@sophiedressel2467]

NOT CLEAr

[@desodenis]

i guess it is linear cuz sinx doesnt have to depend on any y and its derivatives

[@اناقهانثى-ش4ح]

اريد واحد يشرح بلعربي😭😭😭

[@benrow5472]

that's some crazy thing. LOL

[@dominicassia8627]

Great video, would y'+sin(y)=x'+2x be linear? I am a bit confused as to wheather the x' makes a difference, thank you!

[@thepruh1151]

x' would imply that x is a function of another variable instead of y's independent variable. I'm not proficient myself but if I had to describe it algebraically, it would be y_1 + sin(y_2) = x_1 + 2x_2. So there are two distinct variables, in the algebraic case, which are x and y instead of x being the independent variable of y. That's what I'm thinkin' anyhow.

[@kogki9260]

So basically it’s linear if the y is nested in a function

[@abinashmandal6202]

y'=sin(y)..isn't it a linear equation??

[@omnibrain8]

no,but line for y'=sin(x)

[@mohammadzain2047]

Its linear Differential equation...!

[@debjitkanrar7895]

Then in general the degree is >1 ..say this in simple.

[@rubenotter8916]

what. a. cliffhanger.

[@ivancastro365]

Why is the second to the last one not linear?

[@curtpiazza1688]

Best explanation I've seen! 😂

[@poojitha]

Watch this by 1m 43seconds

[@alethealim4379]

If y is in terms of x and If I have third partial derivative of x of (sin(y) y) it is nonlinear right because of the sin(y) * y ?

[@mohammedouallal2]

Last equation is Linear, as the definition : An ordinary diferential equation y'(t) = f(t; y(t)) is called nonlinear iff the function f is nonlinear in the second argument. ref. taken from Gabriel Nagy lecture. sin(x) is a non linear function of course but here we derive y not x.

[@lsjmartin6220]

its really this simple

[@Whoareyou127]

Thanks for making this video, it really helped me a lot!

[@wenkielau4434]

What if is a(x)y'''+b(x)y'=c(x), (is missing out y'' and y in the equation), is it still linear?

[@yaweli2968]

I d c but anyone who dislikes this video has no life.Tbh the dislike button for this video should be disabled.

[@felixhanzen6405]

Is a(x)y''+b(x)y=d(x) a linear DE? Or does it have to include y'?

[@mukulsharma217]

that's a linear equation. although I mistook it the first time. LOL

[@makeitsimpleideas]

Very nice. Please tell me which software you are using in your lectures. It looks very amazing just like hand writing.

[@bl4ckm4mb4f0rlif5]

I believe all the y terms involved in each term of a differential equation is only supposed to contain a just 1 y. Like f(x)y'' + g(x)y' + h(x)y = j(x) Notice the only non derivative y allowed in linear is y^1. And Neither of the y terms are involved in any form of product of y.

[@rahulbanerjee1848]

y'= sin y is it really nonlinear, but how please tell me and send me the answear

[@umarbashir7196]

Thanks for the explanation. It's just nice

[@thelandofworld2983]

last will be linear DQ

[@bl4ckm4mb4f0rlif5]

And i don't think it matters what form the neighboring function of x takes

[@simplicityfx70]

sir could u mention which program you use to write

[@Lefthammy]

Whats the answer lol?

[@yagami0186]

linear

[@AKUJU]

Darude-sandstorm

[@yagami0186]

linear-differentialstorm

[@khattab-iv9189]

+AKUJU 😂😂😂😂😂😂😂😂😂😂😂

[@harrymason8454]

Linear

[@tuamigafannybirds3993]

The last one is linear !!!! :D :D

[@hybmnzz2658]

These are basically linear combinations of the derivatives of y (where the 0th derivative is just y itself) except the scalars are really scalar functions. This is why you see linear algebra applied to ODEs sometimes.

[@TodaysEdition]

You still teaching at UMN?

[@abdullahmalik6127]

Last one is linear differential equation

[@kashmira7754]

You explained it in one go....awesum

[@mohammedouallal2]

Short, clear, nice! This guy apply what we call 'Consistency'!

[@aqsariaz1670]

good video and ans is linear equation

[@rnwillyanto]

thanks for the explanation!

[@bkalrasheed]

The last one is Linear

[@KC-dg9pu]

that's some crazy thing

[@bennybickerton2149]

Fantastic explanation thanks heaps!

[@ahmeraymen2006]

the last one is linear D.E

[@fabianarolemberg8465]

finally a good explanation

[@MadOrange644]

Thank god for KZbin

[@loopuleasa]

this with khan academy helped a lot

[@umerahsan8120]

Linear. You are amazing

[@You_Tube_Watch]

the last one is linear

[@Haneen241]

The last one is linear.. right?

[@arfatx]

3:20 that is not double prime.

[@Dad10100]

I understood everything but i dont understand why y'=sin y is not linear. can you please clarify that?

[@raresgosman1735]

+David Quezada Needs to be of the form ay' + by = c(x) There is no c(x) available to us in that equation

[@Dad10100]

okay i got it. thank you very much

[@Dad10100]

okay thanks man

[@iwuvvparamore]

No, it's non-linear because of the sin(y) term. If we treat "sin" as the coefficient, then it is clear that sin(y) is a function of y, not x. That is why the last expression is first order, non-linear ODE. If c(x) was 0, an expression can still be linear. For example, sin(x)y'' + xy = 0 is a second-order, linear ODE.

[@PraetorianCheese]

"That's some crazy- thing." Hilarious! Thanks for the video, 'twas quite helpful

[@abdulelahalharbi7151]

Its so linear 😂

[@akabanekarma2042]

thanks man cheers

[@muntasirabid1320]

Thank you 🤗🤗🤗

[@sudarshan131]

its useful...thanks...

[@SKINWALKER]

Thank You.

[@abyenegawo456]

KEEP IT UP!

[@randypain4339]

help me a lot.. ty

[@ritikaavadhanula6326]

made my day

[@jackodum9643]

love you

[@AR_BSME]

Sucks '

[@visuallydesigned]

the last one is linear.. Thanks for the explanation!

[@alexjimenez6020]

Very understandable!! thank you very much!

[@Junlee29]

Thank you!! You have no idea how much this helped me.

[@Edwardlannon]

Thanks so much. You are so clear and concise,