- #1
SithsNGiggles
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Homework Statement
The first task was to solve ##(1-x)y''+y=0## about x = 0, which I've already found.
Now I have to use this solution to solve ##\color{red}{xy''+y=0}## about x = 1.
Homework Equations
The Attempt at a Solution
I found the solution about x = 0 (after a lot of rewriting/simplifying) to be
##y=a_0\left(1-\dfrac{1}{2!}x^2-\dfrac{1}{3!}x^3-\dfrac{1}{4!}x^4-\dfrac{2}{5!}x^5-\dfrac{7}{6!}x^6+\cdots\right)+a_1\left(x-\dfrac{1}{3!}x^3-\dfrac{2}{4!}x^4-\dfrac{5}{5!}x^5-\dfrac{18}{6!}x^6+\cdots\right)##
Supposing that's accurate, how can I use it find the next solution?