## Homogeneous now seperable ODE

[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.

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 I realise now, I messed up the integration. The general solution is: y=-x/(ln(Ax^2))

 Tags algebra, homogeneous, ode, seperable