Question

Okay, so I'm given this ODE:

(3xy-2y^2)dx - 7xydy = 0

I chose y = ux, so dy = udx + xdu

So subbing in for y I get:

(3(x^2)u - 2(x^2)(u^2))dx - 7(x^2)u(udx + xdu) = 0

3(x^2)udx - 3(x^2)(u^2)dx - 7(x^2)(u^2)dx - 7(x^3)udu = 0

3(x^2)udx - 9(x^2)(u^2)dx - 7(x^3)udu = 0

I do not know where to go from here in order to be able to integrate (i.e. separate the variables).