Differential equation given integrating factor

[naspek]

Homework Statement

Show that given function μ is an integrating factor and solve the differential equation..

y^2 dx + (1 + xy) dy = 0 ; μ(x) = e^xy

The Attempt at a Solution

let M = y^2
N = (1 + xy)

dM/dy = 2y dN/dx = y hence, not exact equation.

times μ(x) = e^xy to the not exact equations...

2y(e^xy) dx + y(e^xy) dy = 0

let M = 2y(e^xy)
N = y(e^xy)

dM/dy = 2(e^xy) + 2y(e^y) ---> apply product rule

dN/dx = 0(e^xy) + y(e^y) ---> apply product rule

the problem is.. the equations still not the exact equations..
How to proceed?

 

[HallsofIvy]

Yes- which means that $\mu= e^{xy}$ is NOT an integrating factor. Something is wrong with that question.

 

[naspek]

Yes- which means that $\mu= e^{xy}$ is NOT an integrating factor. Something is wrong with that question.

So... i can't solve this equation? the equation doesn't have any solutions?