Math 391 Lecture 18 - Series Solutions to second order linear differential equations contd

In this lecture, we continue our discussion on solving SOLDE using series. We go through several examples, revealing some techniques that we can employ to get to a power series solution.

[teerofive]

I don't know how I found my way to your channel, but thank GOD I did!! I actually learn more from your sessions than I do with my own teacher and PatrickJMT combined. That's the highest compliment that I can give. Subscribed... lol

[MrAHchannel]

You're amazing. Many so-called math teachers should learn how to teach from you!

[Prospitfox]

Omg you explain things more understandably than my teacher does thank you I'm gonna pass my test cause of this video

[xsupercutex]

Oh my god, I see you at city college lol!!! You were a sub for my math 202 class and now this xD...you are very helpful thank you!

[endofkillalon]

omg you just saved my life in my differential equations class! thanks!

[fahmyboy]

Man you are just a great teacher. Keep posting. I think if you also made videos that weren't lecture style, but shorter 12 minute summaries, you'd get tons of views.

[PolishGuy]

You are a great teacher!! I was struggling with Series Solutions for the past 4 days, and your video finally helped me understand!

Thank You!

[m]

Hey I think your recurrence relation at 56:40 is incorrect. I think it's just the a_k should be negative, not positive. Maybe my math's wrong though.

Thank you for the fantastic video. So much help.

[zhiyuxiao]

Great videos!! I think I can answer the confusion about question (a) in the first example:

The derivative of any constants is always 0. So in order to find the derivative of a function at a certain point, I should first differentiate the function and then plug in numbers for x. But not plug in values of x and then differentiate that number. Thus, wronskian should not be 0 and they are linearly independent. @ 27:00

That said, thank you for all of your awesome videos. They are going to save my quarter.

[kristinperez]

Thank you so much you are an absolutely wonderful teacher

[willilow]

Gracias amigo por tu explicación, 100% mejor que mi profesor, saludos de Chile

[colleengillmann]

I have a test on this tomorrow and this was extremely helpful thank you so much! Series are so hard for me to wrap my head around.

[AThomasKent]

You're great! Thanks for posting these :-)

[slaozeren]

I am always taking your course notes and even sharing them with my boyfriend :') Thank you so much!

[spacetimecontinuum]

This was very helpful, enjoyed the full session

[MuddinNYC]

You are so much better than my professor.  I completely understand from you. Thanks

[swanhtet]

When should we assume y= summation a_n *x^n* VS when should we assume y= summation a_n *(x-x_o)^n* ? because sometime it is x, sometimes it is x-x_o.

[HarshPatel-jhyw]

at 29:26 instead of y(1)=2 and yprime(1)=-1, it was y(0)=2 and yprime(0)=-1 or y(2)=2 and yprime(2)=-1, would those conditions also mean that a naught = 2 and a1=-1? or are those only for y(1) and yprime(1)

[ctelwardt]

I am confused at 12:08 when you say you can just shift n=1 to n=0 with no consequences. Can you explain this?

[yasseralharbi]

thank you so much, you'er amazing