I have a problem I am working on:

xy - dy/dx = e^(-3x^2/2) * y^4

If I solve this using the Bernoulli equation then I have n = 4, 1-n = 3.

I make the substitution v = y^3 , y = v^1/3

I'm have a little problem with the next step of finding dx/dy. I'm pretty sure once I find this then I can substitute these values into the DE to get a linear DE that can then be solved.