# Homework Help: Series solution for differential equation

1. Dec 15, 2016

### Sam2000009

<OP warned about not using the homework template>

Obtain a series solution of the diﬀerential equation x(x − 1)y" + [5x − 1]y' + 4y = 0

Do I start by solving it normally then getting a series for the solution or assume y=power series differentiate then add up the series?

I did the latter and got three different but (slightly similar) looking series and the problem asks to group them all into one series which I cannot do

Last edited by a moderator: Dec 15, 2016
2. Dec 16, 2016

### BvU

You have a series for y, e.g. $y = \displaystyle \sum_{n=0}^\infty c_nx^n$ so that $$y' = \sum_{n=1}^\infty n c_nx^{n-1}\quad{\rm {and}}\quad y'' = \sum_{n=2}^\infty n (n-1) c_nx^{n-2} \ ,$$ right ?

Now work out the coefficient of $\ x^n$ in x(x − 1)y" + [5x − 1]y' + 4y = 0

Last edited: Dec 18, 2016
3. Dec 17, 2016

### vela

Staff Emeritus
What's stopping you?