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?
Yes- which means that [itex]\mu= e^{xy}[/itex] is NOT an integrating factor. Something is wrong with that question.