# Homogeneous now seperable ODE

1. Mar 3, 2012

### wtmoore

[Ok so I have transformed a
1st order homogenous ODE into a seperable ODE. However I am having trouble seperating to get y on it's own.

Here's the problem:

du/dx=(2u^2)/x where u = y/x

du/(2u^2)=dx/x <<can't get tex to work

-1/(4u^2)=ln(x)+C=ln(Ax) <<can't get tex to work

1=-4u^2ln(Ax)

1=-4(y^2/x^2)ln(Ax)

y^2=-4x^2ln(Ax)

y=i2xsqrt(lnAx)

Is this algebra correct? Is this the right solution? I'm not sure about bringing the y^2 over to the left is ok.

2. Mar 3, 2012

### wtmoore

I realise now, I messed up the integration.

The general solution is:

y=-x/(ln(Ax^2))