Solving a simple second order DE

**princessmath** · October 22nd 2012, 10:30 PM

How do I solve this

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

How do I start it?

**Siron** · October 22nd 2012, 11:06 PM

It looks easy but it's not because of the coefficient $\frac{1}{2}x$ .
Take a look here:
solve y''+(1/2 x)y'+y=0 - Wolfram|Alpha

**MaxJasper** · October 22nd 2012, 11:14 PM

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

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

**princessmath** · October 23rd 2012, 12:42 AM

WTF?

How do I do it on paper?

Thread: Solving a simple second order DE