Solving a homogeneous first-order ordinary differential eqn

[Aceix]

Homework Statement

dy/dx = (x+4y)²

Homework Equations

The Attempt at a Solution

I substitute y=ux, where u is a function of x, and I'm not a ble to solve. My intention was to arrive at a seperable form, but I'm not achieving it.[/B]

 

[ehild]

Try the substitution u=x+4y.

 

[LCKurtz]

@Aceix Your problem is assuming your DE is homogeneous. Homogeneous in this sense means $f(tx,ty) = f(x,y)$. That does't work for $f(x,y)=(x-4y)^2$.

 

[Aceix]

Thanks a lot! I've got it now.