Question

Solve the DE (x^2-2x+3) y''+18xy'-9xy=0 using power series

Answer 1

what class is this?

Answer 2

differential equations

Answer 3

Let \[y=\sum_{n=0}^{\infty} a_n x^n\]
Sub into DE:
\[=\sum_{n=2}^{\infty}n(n-1)a_n x^n -2\sum_{n=1}^{\infty}n(n+1)a_{n+1}x^n+3\sum_{n=0}^{\infty}(n+2)(n+1)a_{n+2}x^n\]
\[+18\sum_{n=1}^{\infty}na_nx^n-9\sum_{n=1}^{\infty}a_{n-1}x^n=0\]

This is where I am stuck! Any help?

Answer 4

About \(x=0\), I presume?

Answer 5

Yes it is

Answer 6

any help?