# Solve by power series.

• Sep 26th 2011, 06:16 PM
cheme
Solve by power series.
I am trying to solve the following DE by power series method.

$\displaystyle x^{2}y''+5xy'+(x+4)y=0$

I am assuming a solution of $\displaystyle y=\sum_{n=0}^{\infty }c_{n}x^{n}$

Making all the proper substitutions, I keep getting 0 for all my constants. I know this has to do with not making the proper substitution but do not know how to try something else.
• Sep 26th 2011, 07:15 PM
Prove It
Re: Solve by power series.
Quote:

Originally Posted by cheme
I am trying to solve the following DE by power series method.

$\displaystyle x^{2}y''+5xy'+(x+4)y=0$

I am assuming a solution of $\displaystyle y=\sum_{n=0}^{\infty }c_{n}x^{n}$

Making all the proper substitutions, I keep getting 0 for all my constants. I know this has to do with not making the proper substitution but do not know how to try something else.

Could you please show your working, then we might be able to tell you why all your constants are coming out as 0...