Homogeneous Second Order Linear Differential Equations

[bmgag19]

how can an equation be second order and linear. If it's second order, it has X^2 and therefore it could not be linear.

[macky191]

Thanks Patrick, you're a great teacher.

[patrickJMT]

@macky191 thanks : )

[liamreidy7]

explained brilliantly as usual

[jimauSL]

please can you solve y"+9y=e^X?? thanx alot=)

[vampiracy]

@jimauSL

First solve y''+9y=0 [you can do that using techniques learned in this video], that will get you your complimentary solution c(x). Then use the the method of undetermined coefficients [here's the code for the video in which Patrick here talks about that: /watch?v=_U8Y5z-kVvI] to find your particular solution p(x). Your final solution is y(x)=c(x)+p(x).

[Muk6361]

How do you solve a homogeneous second order linear equation when the coefficients are not constants. when they are functions of x. (non constant functions of x)

[khanee2877]

lol u have censored they naked women image behind you on your Profile Picture :D

[patrickJMT]

@khanee2877 yes, strange people were offended by a naked mannequin and i had to change it!

[soft0717]

Thank you~~ ~ helps a lot~~~

[megabenman]

can i donate or something, it makes me shudder to think how much my teachers get paid when you your youtube videos help me so much more

[patrickJMT]

@megabenman visit my website, click on a video and a donation link pops up : )

[XzcutioneR2]

patrick, buddy, you're an asset to this world!

[patrickJMT]

@XzcutioneR2 just doin' what i can : )

[kvstud42]

We've been doing this in class for the last 6 weeks, so I hear... I also heard that I have a test tomorrow. My instructor has a verrrry heavy accent, and stumbles so much over his english, it's tough understand his point. Although he is a genius, he could not break it down to be so simple, like you do. After two hours of study time, I feel confident going into tomorrow's test without having been to my last 10 lectures.

[JacKaYu]

You explain it so much better than in my math class! Thanks! :)

[STEFIzeADVENTURER]

i never pay attention in class cuz i just absolutely hate calc, but my midterm came and i really needed to learn half a semesters worth of calculus and i somehow managed to cram 3 hours worth of calculus using your videos as a guide. I think i might have passed the exam....thank you soooo much!!!!

[drrojas]

You are the reason i did well in Calc 1 , Calc 2 , and now ODE's and Linear Algebra. Thank you! you're the bomb.com

[patrickJMT]

@drrojas glad i could help you out so much

[drgrrlfriend]

This is wonderfully helpful. Thank you for posting it.

One suggestion, I would like to see how to handle initial conditions [not just in terms of y(x), but y'(x) as well] within homogeneous second order linear differential equations, as I know many people here, including myself, know how to solve using initial conditions, but just don't realize it. It wouldn't need to be a long video, maybe just a short example using one of the equations from this video.

[pimpmymail]

You rock AND rule, and got paper on the screen !!! So you win !!!

( Studying's comical mood arrived )

[JaktheAtheist]

I know you hear this a lot, but thank you so much for doing this. I major in physics, and there is no way I would be able to slug through the math without your videos.

I hope you can put up some vidoes of example problems for differential equations for the next dif eq student that comes along.

[patrickJMT]

@JaktheAtheist i still like to hear it : ) happy to be able to help you.

[ogamer666]

see how it jumps from 360p to 1080p!!?? HD FTW

[GHO5TeZ]

love your videos, they've helped my so many times. Keep up the good work :D

[JohannVF]

I think you just saved my bacon, in DE.

[patrickJMT]

@JohannVF mmmmmm bacon

[Shockwave231]

@patrickJMT Lol....just lol

[omrodez]

I love all of your videos! and by the way its pronounced, (hoh-muh-jee-nee-uhs)

[MuikJuaggre]

Math 2Z03 Anyone? ;)

[aarchas]

@MuikJuaggre LOL

[MrMymusicality]

Why was there an x in the last answer next to c2??? It's the answer, I know, but why is it in there??

[PumpinIron84]

you really make math simple!!!

[honeypot11]

o gosh at this point with my math courses i'm just like "yet another formula to memorize in a limited amount of time" -.-

thank you so much though for these! really helps c:

[THESILVERNARUTO]

Can you show me one with solving with initial conditions?

[EthanRDale]

chears man helped heaps

[Pianoblacks]

i love your american accent on homogeneous lol.

canadian = "homo" "genius"

[soosayaay]

I like u ,,, direct and simple :D

[eiffel0108]

You'd be surprised how interesting this looks, even though I have no left brain.

[vallthat]

what's the difference between a general solution and a particular solution???

[vallthat]

what's the difference between a general solution and a particular solution???

[TheJuga]

Haha homo equations

[SuperPowderkeg]

God give you all the blessings under the sun!! You sir are a legend!!

[shirishsam08410447]

Hey bro, gr8 videos, have u uploaded any video solving second order differential equation with initial conditions, let me know

[xgamer2100]

those homo equations are fing sukng my brain out

[brco2003]

Do you have the complex case posted?

[AMHMusicStudio]

big help man...thanks for the videos...keep it up!

[tehn00bpwn3r]

I need non-homogeneous!

[ViggyNash]

Could you do a video on series solutions for second-order differential equations?

I've gotten 0 out of 3 questions right on my homework, so I obviously don't know what I'm doing.

[AromaVancouver]

How to solve 2nd Order Linear Homogeneous ODE with Variables Coefficients which is not a Cauchy-Euler equation. For example, y'' +(x^2) y' +(x^3) y = 0.

[Deltad]

@AromaVancouver convert it to a constant coefficient by reducing it to a first order ODE

[exussum5]

a explanation in terms of where the r term come:

if our ode is a*y''+b*y'+c*y=0

if we try y=e^rt then

y'=r*e^rt

y''=r^2*e^rt

subing this into the equation gives a(r^2*e^rt)+b(r*e^rt)+c(e^rt)=­0

as e^r will never equal zero we may divide this out

giving a*r^2+b*r+c=0

o and my textbook uses lambda instead of r

[nickoborn]

thank you for this.

[abojakee]

hey :)

do u have vedios for higher order linear ode ?!

plz need help

thx 4 ur vedios !!

[BronxBounty]

again. thank you!

[Bato1110]

I have been using you since calc 3 ur amazing!

[flurgemasterflex]

i just want to know what is an auxiliary equation using the variable r? i have a homework question that asks forthat and i have no clue what that is. but thanks for the video

[Holyfrik1]

what do you do if u have a constant term.

[juanpablodonche]

thank you so much

very useful for studying

i really apreciate your time for doing this

good luck

[NoobyJumper]

i hope you teach in my school, you are way better than the professor i am having for differential equation right now :(

[YostRS]

Thank you for your help so far!

[ppingpoong]

great stuff dude! learnt this stuff 2 years ago but never had to use it until now. found this amazing revision!

[Chrismbo]

Clear and simple explanation - well done!

[webmastertool]

I love differential equations.

[fizzmaverick]

euler cauchy anyone??

[flopmeaset11]

hey can you make a video how to verify you answers. E.g. sub y" and y' and y into the original equation to prove that your solution is correct...i have to verify my results in a home work question and I dont really know how to!! your help would be sweet.

[SerielThriller]

awesome

[elight07]

Thanks!!!

[TavarishReyes]

Great Patrick, It will be great to have a mix of iTunes University and Wikipedia, where people like you can post lectures, notes about Mathematics, suppose about game theory, linear algebra and so on...

[kudakadere]

how old are you??

[aidowalsh666]

if we had initial conditions... would they be subbed in at c1 c2? also one of my initial conditions is x(0)= 0, so it effects my answer what root i pick as r1, do you know what i do here?

[aidowalsh666]

@aidowalsh666 figured it out dont heed me...

[firativerson]

great video! thank you

[supuwamigosh]

you r a great man.

[MICHAELMEMISBACL]

Anyone love the annihilator method?

[patrickJMT]

thank you for your useful comment

[likasombodie]

@ErayTarrell what game?

[Platemaster]

@ErayTarrell Maybe you YouTube is trying to tell you something...

Like you should have never left the high school...

[2ubelazy]

when r= +/-1, is that the repeated single root, or are they distinct?

If they are distinct then what is a repeated single root?

[shannigammi]

@2ubelazy

i think if r=+/-1 then r1= +1 and r2 = -1

if they were repeated then itd be r1=+1; r2=+1 (such as (1-x)^2=0 )

[Moonbladez123]

tnx

[quifred]

Leftie ftw!

[seph1252]

They say Left handed people tend to be smarter. somehow I tend to agree with them a lot of smart people I know seem to be lefties. If I learned to be ambidextrous would that make me smarter?

[talzz88]

heey

just wondering, if the equation is equal to say : 13cost + sint rather than 0, how would you solve it ?

[EFGX]

great, thank you !!

[baashish]

its not linear anymore...

[TaroQuispe]

dude, tnx a lot for this, midterm in two days!

[BKproduction1906]

Super awsome thank you man :)

[JSSTyger]

I'll give somebody a cookie if they can solve this nonlinear equation

y''+(x/2)y'-y=0, y(0)=2, y'(0)=0

Hint:  use power series

[rizza123]

Can some1 plz answer this qu..i just want to check my answer.

16y" - y = 0

[JSSTyger]

the solution is Ae(x/4)+Be(-x/4)

[rizza123]

Eyy Thank u very much

[amyrayhe]

haha i know what you mean. I only discovered these videos last night, at 1am, and my exam is in 2 hours hahahaah

[nodhear]

I'm taking Linear Algebra II right now. As far as going from ay'' + by' + cy = 0 to ar^2 + b^y +c = 0, I don't have this in a book because my professor isn't using a book. He seems to think because I'm a senior I should know this already (maybe I should), but the table shown at 1:29 was very helpful. He did go over it in class once, but thanks for posting it again. I needed to see it again for it to make sense. THANK YOU!

[MRIYBR]

I do appreciate your posting all these videos. BUT you have missed out on very important topics such as homogeneous FIRST ORDER diff. eqs, fourier series and many more. If you could add those videos, I bet you'll get at least 2000 more subscribers in a day (as all of imperial college's students vould subscribe). Give it thought please!

[aahvr6]

Homogeneous first order are easier than second order. You have a single r and a single number. Subtract from both sides to get r = whatever.

As far as the others, I would also love to see some more involved things in differential equations.

Oh, and Patrick? You got me an A in my Cal 1 and Cal 2 class and now you're helping me get A's in diffy and Cal 3. I can't express how much I appreciate these videos. I really don't understand why it's so hard for teachers to explain these logically.

[boydekus]

Thank you very much

[ShadyMan01]

Sorry, ignore my previous comment, I just found it!

[itsdouge]

where did u find the non-homogeneous vid?

[ShadyMan01]

Method of Undetermined Coefficients/ 2nd Order Linear DE.

It's by Patrick, it goes over 2 vids!

[ShadyMan01]

Do you have any examples on the non-homogeneous case, thanks!

[nikola29091989]

How do you work out the factors for example 1 to get (r+3)(r-2)=0 - i tried using the quadratic equation but couldnt do it.

[yetipoo]

i used the quadratic equation......it does work..maybe you messed up some how :s

[geekyjj]

hey Patrick,

Your videos are very helpful! But could you add some videos on second order differential equations( by method of undetermined coefficients) and other second order non homogeneous differential equations?

[geekyjj]

thanks

[xbox360gamer2008]

Thank you so much, this is a life saver!!

[morrillchawaii]

dont understand the non homogeneous equations the y sup p using the G(x) function

[sparty007]

I think it's spelled homogeneous

[patrickJMT]

absolutely... let me fix that now : )

[patrickJMT]

thanks... nothing annoys me more than a spelling mistake

[sparty007]

thanks for the video, because i have a calculus exam tomorrow and i needed to clarify my understanding, and your video is very helpful. I sure hope i have your knowledge going in to the exam (calculus 3)

[JohnBlack345]

@patrickJMT Yeah, it's pronounced as ho-mo-gee-nee-ous.

[varvijviju]

y"-c(1+be^(a(Xf-X))y=0

With initial and boundary conditions.

y=P(x)

dp/dx = 0 @ X=Xf

P=Pw @ X = 0

c= u/(Kfhw)

Need final solution in the form of P(x)

Thanks much

[kopboi99]

@sparty007 im a homogenius

[chezzman]

Can you do a non-homogeneous version?

[Syruscleat]

Dude, you're such a Math Geek, but I love you...

[TimPetrovich]

Thanks Patrick, another good video. Could you please do a video of applied maxima or minima problem? Thanks a lot man.

[patrickJMT]

i have some optimization videos (i think)

[MathMikie]

yeah he does i seen them one day when i was looking at the videos

[ravegreen]

Very helpful, Thanks!!

[MathMikie]

that was very helpful please do an example where the roots are complex so i can see how those work as well

[patrickJMT]

ok, i will do one later : ) going to go have lunch and enjoy a beautiful november day in austin for now : )