Determine ( ylny - e^(-xy) )dx + ( 1/y + xlny )dy = 0 is exact or not. If exact it, solve it.

Answer 1

Mdx + Ndy = 0 is exact if dM/dy = dN/dx

M= ylny -e^(-xy)

N = 1/y + xlny

dM/dy = 1 + lny +x e^(-xy)

dN/dx = lny

to make it exact requires an integrating factor