I'm trying to complete a practice exam for a class, but I'm having problems verifying my answers. I looked online, but I couldn't find any applet that calculate power series solutions to equations easily, so I thought this would be the best place to ask.
The equation is (4-t2)y''+2y=0
The recurrence relation I calculated is an+2=(an(n2-n-1)) ⁄ ((n+2)(n+1))
I calculated y=a0(1-(x2 ⁄ 2)-(x4 ⁄ 24)+...)+a1(x-(x3 ⁄ 6)-(x5 ⁄ 24)+...)
Sorry for any formatting issues; that's the first time I've used html in awhile. Does that solution look right at all? Thanks in advance for any help.
Perhaps check your calculation again. \begin{align*} 4a_{2}+a_{0} & =0\\ 12a_{3}+a_{1} & =0 \end{align*}
\begin{align*} a_{n+2} & =\frac{n-2}{4\left(n+2\right)}a_{n},\quad n=2,3,\cdots \end{align*}