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?