Originally Posted by

**nameck** 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

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?