# Solving a homogeneous first-order ordinary differential eqn

1. Apr 20, 2016

### Aceix

1. The problem statement, all variables and given/known data
dy/dx = (x+4y)2

2. Relevant equations

3. 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.

2. Apr 20, 2016

### ehild

Try the substitution u=x+4y.

3. Apr 20, 2016

### 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 $f(x,y)=(x-4y)^2$.

4. Apr 20, 2016

### Aceix

Thanks a lot! I've got it now.