Power Series Solutions of Differential Equations

[melisantika]

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[Onepissite]

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[Ondelendo]

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[bebeheuy]

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[willamricard]

Nice Video That You Share , So Very Nice Thanks You Power Series Solutions of Differential Equations - In this video, I show how to use power series to find a solution of a differential equation

[imegatrone]

I Really Like The Video From Your Power Series Solutions of Differential Equations - In this video, I show how to use power series to find a solution of a differential equation

[ozgur716]

THANK YOU VERY MUCH FOR THE VIDEO!!!

[bugzo0]

I think the recursive formula for Cn has to be Co/(n+1)!

for n=1 it's 2!

for n=2 it's 3! and so on....

[MizuPsi]

Great video, but I think the example is pretty basic. If you are looking for a good example problem that is more advanced, y'' - xy' - y = 0 is one that's been giving me a ton of trouble. I'm not asking you to solve it for me, but it is presenting a number of things that happen in the higher difficulty series expansion problems.

[patrickJMT]

@MizuPsi i only know how to do simple examples

[RiemannXiFunction]

@MizuPsi Wolfram Alpha can solve this equation and there's a Show Steps button.

[patrickalle]

Hey Pat. At the end of your video you're basically saying "oh, well this is basically e^x." Which brought Laplace Transforms to mind. Where you have to recognize what whatever the thing is and plug and chug. Are these related or just coincidences?

[23youwatch]

is there a second example video?

[evelelamayo]

the answer is Co/(n+1)!

[hocka09]

@evelelamayo yeah, I was wondering about that...

[yorkeR177]

@evelelamayo I don't believe so. If you check, he arrived at the condition: C_(n+1) = (C_n)/(n+1). He then wrote his answer in terms of C_n, so (C_0)/(n!) is the correct answer. This is actually a famous example because y = ce^x (constant c) is the only function where y = y' (I think).

[Wabball]

Hello, so I am in Calculus II and we are doing series along with some things from the previous section. I have a problem dy/dt=t(2y+5), with the initial condition y(0)=1. How do I go about solving this? What do I solve for?

[banditontherun1024]

@Wabball calculus two? huh well you have a separable equation so you can do (2y+5)dy =t dt and then integrate both sides.

[JSSTyger]

I knew the answer right when I looked at it. :)

I actually did not learn power series methods for solving diff eqs in college. I taught it to myself afterward in my spare time.

[judowrestler1]

hey just wanted to say thanks,  you made teaching myself Diff Eq. a lot easier.

[humphrec73]

a more complex example? Is it available yet?

[Shery919]

thanks brother

[Haroson]

Do you have boundary Value problem videos? :/

[tfreed20]

I followed everything you did and it make sense, however i had one question. you say C_n= C_0/n!, but if i was to use your work above and plug in say 2, then C_2 should equal C_0/2!. This isn't what you calculated C_2 to be equal to previously in the problem. Should C_n not equal C_0/(n+1)! ???

[sushiserv]

@tfreed20 Yea, I was thinking the same thing. if n=2, and C_0 @ n=2 submits C_0/3!, shouldn't it be (n+1)! ?

[JSSTyger]

@tfreed20

I can clear up your question. When he had Cn+1 = Cn/(n+1), the equation was in terms of Cn and not of C0. That is why the multipliers were not the same. Plugging in n = 1, you get C2 = C1/(2) = C0/2.

It actually is the same.

[donalddaizy]

nice, but not up to the mark because in exams questions were too complicated, not simple as y`-y=0

[Biotasm]

I need some IVP and maybe some second derivatives in there! Please and thanks! I am a freshmen who just started watching you because you are the most informative I could find! :)

[Jdiddy1792]

NEED MORE DIFFERENTIAL EQUATION EXAMPLES PLEASE

[gvsfgdf]

This is why I subscribed to you dawg...

[tehsuanhaha]

Can you do second order ones with IVP??

I've been following you since high school and now Im in engineering, but still watching you! you're awesome, thanks

Pleasee and thanks

[sandysanchez4]

more complicated problems! :)

[thephlebotomist]

could we see some of important ODEs that need this approach like a bessel or airy function?

[Dosalt]

I like to see a harder example solved

[boities]

Hey so I got this problem where i'm suposed to do power series solving for a DE and the equation is

y' = y^2 + x^2

so I use the general thing where y = series thing

but what do i do with the x^2?

[MrIndifferent89]

patrick please make more of these, im so lost with my teacher's horrible explanation!!!!

[staM034]

nice Σ symbol ...

[liquidstl]

I'm taking an engineering math class this fall so I'm watching some of these videos as review. One thing I was never too sure of is. When shifting the index; is the point to have the index start at the same point for each series, or to have the same exponent so that you can factor out the Cn's and equate coefficients to solve for the recurrence relation? Also, Its slipping my mind at the moment, but other than inspection, what other way is there to solve this ODE?

[Thexder0]

@liquidstl Yes, you first shift indices to match the exponents in x. If after that, the sums start at different points, **do not** shift -- just write separately the few indices which are not in all the sums.

That said, great video!

[dwilmer7]

thank you.. one more question.. after you take derivative of first summation (n=0 to n=infinity).. why does it then change to n=1 to n=infinity?? thank you

[indispens]

@dwilmer7 because the first terms is constant and the derivative of a constant is zero

[dwilmer7]

patrick didnt you say you did a more complicated example?? cant find it? thanks

[patrickJMT]

@dwilmer7 i had every intent to when i made this, but i never did yet

[bobyoco]

@patrickJMT I second the idea of another video even though I have my test soon. This was the hardest for me to learn/understand. As always, you're a lifesaver Pat!

[bucknut017]

I so despise these problems

[lifematch]

isn't so pose to be Co/(n+1)!

[PaperChaser01]

@lifematch i was/am wondering that too...

[PaperChaser01]

@lifematch nvm, i see what he did. its for Csub1,2,3... not for n=0,1,2,3 because that n was for the Csub(n+1) terms or sums (idk what to call it)

[MrCoffee2004]

@lifematch I am currently wondering that myself...

[MadenKenya]

Nice vid Patrick! Have you uploaded any video showing series solution of ODE in a forced case?

[liquidstl]

Hey could you do a more complecated example of this? thanks

[Zeeblog]

Thanks, this really helped, your teaching method is really clear and concise. I also like the way you make your summation signs, haha.

[96phillies1]

Thank You I Need This For My 7th Grade Math Test

[mtnedu]

YILDIZ TEKNİK ÜNİVERSİTESİ

[derrick9006]

Patrick can u hlp me i donno how to solve this question

If y = ( x^7 - x^3 + x ) / x^5 find dy/dx.

Plz hlp he .

[gerhdez]

@derrick9006 dude just go to wolfram alpha

[reaseher]

hello i m seher i m the student of BCSC hons n hving problem in mutivariable calculus can u plz load some lectures related to tht like how to solve ellipse and such type of problems thank u n plz kindly load ur videos titled with proper name and serial wise lecture number thank u.

[mous221]

I love youtube

[dave3030]

Thanks for this, post that harder question! In your next video can you explain how to find the first few nonzero terms "about x=0"?

[MadMath44]

very nice. The record quality of your videos are better then mine, what are you using Pat?

[patrickJMT]

i use the cheapest $15 headset microphone that i could find...

[patrickJMT]

and the cam was a $100 webcam by logitech

[MadMath44]

are you using logitech pro-9000?

great videos, excellent teaching, God bless you

[patrickJMT]

it is: QuickCam Orbit AF

[dave3030]

You should turn off the auto brightness/contrast so the whole video doesn't flash brightness when your hand goes into view.

Thanks!

[patrickJMT]

thanks for the tip!

i will do this

[atifrocks]

Has anyone ever told you that you are absolutely amazing!!!!!!!!!!!!!!!!

[henricamara111]

hey Patrick...

would u please explain how to sole Exact Differential equations?

Thx anyways,

[henricx1]

i tried this method for y+y'=0

I got c_n = - c_0 / (n)!

I thought when you came to the summation, you could just factor out the -1, then I got y= C* -e^x, but it should be C* e^-x

what did I do wrong?

[wirsindheldenowns]

@henricx1 i'm trying to do that for HW, my c_n = [(-1)^n* c_0] / (n)!

stillworking on it

[stokes181]

boooom I love it! Thank you!!

[henricx1]

omfg this is cool

[Syruscleat]

Wow! You made my hat spin with all that algebra! As always, my hat goes off to the AMG! American Math Guru that is!

[patrickJMT]

no, there is no mistake!

[TheTokinotabibito]

Oh,I'm sorry.

[patrickJMT]

do not be sorry! i make mistakes quite regularly!!!

actually, i appreciate it VERY much when people point out my mistakes - i do not want incorrect videos! as i say, feel free to post comments or questions : )

this is how we all learn! : )

[TheTokinotabibito]

I see!

Now　I understood　Cn＝C0 / n!.

[TheTokinotabibito]

I'm very sorry that I sad a wrong thing....

[JFlopex]

I think Cn should equal C0/(n+1)!

Cn=C0/(n+1)!

[patrickJMT]

nope, it is correct

[StillAware]

No, if you see at about 08:15, he erased the C_n+1 = and wrote Cn=... so Patrick is right. Good video. Very well explained.

[VelocityCCX]

Thank-you Patrick, this is my first of I hope many video's I will watch.

[elpueblano009]

lol did get it

[pascalcarlos]

cn = c0/(n+1)! ?

[patrickJMT]

nope! c_n = c_0 / (n)!

[Sitara04]

how are assumptions made? How do we know what the assumption should be?

[pabloMTv]

another thing learned :D

[pleih]

Over 9000

[CollegeLoheart]

What level is this?

[patrickJMT]

differential equations - usually taken after calc 2 or 3

[CollegeLoheart]

Seems easy. Thanks.