# Math Help - Solving a simple second order DE

1. ## Solving a simple second order DE

How do I solve this

f''(x) +(1/2x) f'(x) + f(x) =0 ??

How do I start it?

2. ## Re: Solving a simple second order DE

It looks easy but it's not because of the coefficient $\frac{1}{2}x$.
Take a look here:
solve y&#39;&#39;&#43;&#40;1&#47;2 x&#41;y&#39;&#43;y&#61;0 - Wolfram|Alpha

3. ## Re: Solving a simple second order DE

If that is $\frac{1}{2x}$ then:

$f(x)=c_1 \sqrt[4]{x} J_{\frac{1}{4}}(x)+c_2 \sqrt[4]{x} Y_{\frac{1}{4}}(x)$

4. ## Re: Solving a simple second order DE

WTF?

How do I do it on paper?