Solving a Differential Equation with a Substitution

[FeDeX_LaTeX]

I have the differential equation:

$$4(2x^2 + xy) \frac{dy}{dx} = 3y^2 + 4xy$$

The only thing I could see working is a substitution, but I can't work out which one to use. I've tried letting v = xy, or v = y/x, but neither of those seem to produce anything useful. Can anyone give me a hint?

 

[Paintjunkie]

i thought it was supposed to be y=xv... that's for the homogeneous ones i think. i am not expert though i am in the class right now myself.

 

[FeDeX_LaTeX]

You're right, y = vx does work... sorry, idiotic me didn't even check it properly. Thanks!

 

[D H]

Refactor the left hand side to 4x(2x+y)dy/dx. This suggests trying u=2x+y. This will simplify nicely, and should in turn suggest trying v=u².

 

[FeDeX_LaTeX]

Thanks, that worked out even better -- I think that may have been the intended solution.