# Math Help - Solving Differential Equation - series solution

1. ## Solving Differential Equation - series solution

Hi All;
let $a_{0} \neq0$ and $a_{3} \neq0$ and

$a_{n} =\frac{(n-3)a_{n-1}}{(n-2)(n-1)-2};n\geq1$
I need the general formula for the following summation in terms of $a_{0}$ and $a_{3}$

$y=\sum_{i=1}^{\infty}a_{n}x^{n-2}
$

Thanks

2. I would simplify the expression multiplying the $a_{n-1}$. I think you'd find everything much easier to deal with.

3. ## Like the man before me...

said...

$a_n=\frac{(n-3)a_{n-1}}{(n-1)(n-2)-2}=\frac{(n-3)a_{n-1}}{n^2-3n}=\frac{a_{n-1}}{n}$