# Solving a simple second order DE

• Oct 22nd 2012, 10:30 PM
princessmath
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?
• Oct 22nd 2012, 11:06 PM
Siron
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
• Oct 22nd 2012, 11:14 PM
MaxJasper
Re: Solving a simple second order DE
If that is $\frac{1}{2x}$ then:

$f(x)=c_1 \sqrt[4]{x} J_{\frac{1}{4}}(x)+c_2 \sqrt[4]{x} Y_{\frac{1}{4}}(x)$
• Oct 23rd 2012, 12:42 AM
princessmath
Re: Solving a simple second order DE
WTF?

How do I do it on paper?