How To Solve Almost Exact Differential Equation

The general form of an exact differentiatial Equation is Mdx+Ndy=0 Where M = ∂F/∂x and N = ∂F/∂y Given that ∂M/∂y= ∂N/∂x Some times the equations above may appear to be non-exact differentiatial Equation when ∂M/∂y≠∂N/∂x In that case, we have to multiply the equation by some factor, a function μ(x, y), which will make it exact differentiatial Equation. When this function μ(x, y) exists it is called an integrating factor. It will make valid the following expression: ∂(μ·M)/∂y= ∂(u·N)/∂x