(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Find the general solution near x = 0 of y'' - xy' + 2y = 0 (using power series).

Answer:

y = a_0 * y_1(x) + a_1 * y_2(x)

where

y_1(x) = 1 - x^2 and y_2(x) = x - 1/6 * x^3 - 1/120 x^5 - 1/1680 * x^7 - ...

2. Relevant equations

Power series. Sigma notation for summations. Polynomial derivatives.

3. The attempt at a solution

My attempt is attached. I get y(x) = ke^x and I think I'm wrong but I'm not sure since the answer my book gives doesn't use sigma notation.

I'd appreciate if someone could tell me if I'm right or wrong and if I am wrong, where I went wrong.

Thanks in advance!

**Physics Forums - The Fusion of Science and Community**

# Finding general solution to a differential equation using power series

Know someone interested in this topic? Share a link to this question via email,
Google+,
Twitter, or
Facebook

Have something to add?

- Similar discussions for: Finding general solution to a differential equation using power series

Loading...

**Physics Forums - The Fusion of Science and Community**