How do I approach this nonlinear diffeq?

[MackTuesday]

I'm fiddling around with complex roots of polynomials and I'm faced with this:

z' P(z) + Q(z) = 0

Here P and Q are any polynomials with real coefficients and z is complex. Any ideas on how I might start on this?

 

[lewisje]

if z' means "dz/dw" then this equation is separable