I've been having some real trouble solving this differential equation, mainly because I can't figure out what method to use. The question is as follows:

Consider the differential equation:

$\displaystyle (x^3/y + 3/x)dx + (3x^3 - x^4/(2y^2) - 1/(2y))dy = 0$

a) Show that the given equation is not exact.

b) Find constants a and b for which $\displaystyle t(x,y) = x^a*y^b$ is an integrating factor for the given equation.

c) Use part b) to solve the given equation.

I think it's easy to show that the ODE is not exact but I'm not sure how to do the rest...

Thanks a lot,

AK