Power Series Solutions of Differential Equations

Solving Differential Equations Using Series Solutions: Step-by-Step Guide
In this video, I demonstrate how to find the solution to a differential equation using series solutions. We'll explore the method of substituting a power series into the differential equation, solving for the coefficients, and understanding the process behind finding solutions for equations of this type. Ideal for anyone looking to deepen their understanding of differential equations and series techniques.

What You Will Learn:

How to apply a power series approach to solve differential equations.
Step-by-step instructions for finding series solutions to first-order equations.
Practical insights into using series expansions in calculus and advanced mathematics.
If you find this video helpful, be sure to subscribe for more mathematics content, comment with any questions, and like & share with others who might benefit from these concepts.

Support My Work on Patreon:

#DifferentialEquations #SeriesSolutions #PowerSeries #Calculus #MathHelp #PatrickJMT #InfiniteSeries #MathTutorial #SeriesMethod

[mrzzoz]

this guy will go straight to the heaven 

[kaizhang]

Patrick, I just want to take my time to thank you for all the great videos on your channel. I am a struggling engineer but thanks to your videos, i've been passing all my math classes with ease. I really wish that you have more advanced contents or covered more topics beyond simple calculus such as fluid mechanics or statistic analysis so that i can breeze through all my courses. It literally takes me 5min to fully cover a topic compared to 2-3 hours by looking through my textbook.

Anyway keep doing what you do.

[Magnawulf]

For anyone wondering why it's not Cn = Co/(n+1)!

Look at his equations. For example he determined that C3 = Co/3! which is indeed Cn = Co/n!. He also determined that C4 = Co/4! which follows Cn = Co/n!

[tonystank]

My man, @PatrickJMT is helping a lot of people.... Especially during their exams!!! Thanks man.

[hampsternips]

my lecturer is a potato, Patrick you are awesome! 

[heilgid]

the man, the myth, the legend... patrickjmt

[magaliebravo]

I'm pretty sure its suppose to be c/(n+1)!
either way, thanks for uploading PatricJMT!!!
I've been following you since my algebra days. <3

[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! : )

[JustinZymbaluk]

Thanks a lot Patrick, you've been a real life saver my entire college career. I also just want to say, I love the way you write your sigmas, they look so cool and sleek!

[Ammaray]

Would you be willing to post a couple more examples of Power Series solutions of DE with initial conditions, possibly in a term-by-term method? Thanks for all you have done. You have helped me so much already! I have been learning from your videos for a couple of years now.

[GenaEnSamIAm]

Hey Patrick

You are the real MVP dude.
Thanks for all you've done!!

[dangerousangel]

I am laughing when he said at the end, “hopefully this looks familiar to you” 😂 and I’m just like, “he means that’s e^x right?” Lol and lol yeah.

I hope it looks familiar to me on that final exam next week

[mosulicwele]

I passed the maths because of your efforts, may all the blessings be upon you. Thanks!!! You always make things easier so that we can understand.

[patrickjmt]

differential equations - usually taken after calc 2 or 3

[Zeeblog]

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

[MrSexyJem]

patrick, for the people who are going to have trouble in the near future, i really suggest that u put up another example one with x's and y's because those question really needs a next level of understanding. For example y'' - xy' - y= 0 really suggest you put up on any of these type of equations. it would really help us out alot.

[DaveDruska]

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

[virginialikesyou]

patrickJMT you have helped me from Calculus I all the way through Differential Equations. I LOVE YOU!!

[TazerBlaze]

When you differentiate a summation, imagine differentiating every term in the summation.
He changed it because if not then, you would start at n=0 for all terms in the summation so the 1st term would be C0*x^-1 which would not be the derivative of ANY of the terms so it would not be in the summation, that's how it has to be rewritten (:

[Arwokid]

because (if im not wrong) ...a power series has to start with x^0 (<- first term), therefore, when you take the derivative where it's x^(n-1), you have to make n start at 1.

hope that helps!