# differential equation given integrating factor

by naspek
Tags: differential, equation, factor, integrating
 P: 181 1. The problem statement, all variables and given/known data 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 3. 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?
 Math Emeritus Sci Advisor Thanks PF Gold P: 38,904 Yes- which means that $\mu= e^{xy}$ is NOT an integrating factor. Something is wrong with that question.
P: 181
 Quote by HallsofIvy 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?

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