Question

@Kainui What advantage does the Power Method have, over the auxiliary method?

Answer 1

Well here's a particular equation:

y''+xy=0

It's fairly easy with a power series, but I don't know of any other way to solve it off the top of my head. The power series approach lets you solve quite a bit of differential equations and then you end up with either power series of functions you already know, but sometimes you'll get power series functions that aren't defined as normal functions really.

For example, if we never discovered sin(x) we'd have to use the power series every time it came up.

Answer 2

http://www.sosmath.com/diffeq/series/series04/series04.html

Answer 3

Thanks :)

Answer 4

Also, power series is fun. That's why I like it haha.

Answer 5

lolz i agree