1. Verify that the given differential equation is not exact.
(x^2 + 2xy − y^2) dx + (y^2 + 2xy − x^2) dy = 0
2. If the given DE is written in the form M(x, y) dx + N(x, y) dy = 0, one has:
My =
Nx = .
Since My and Nx equal, the equation is not exact.
3. Multiply the given differential equation by the integrating factor μ(x, y) = (x + y)^−2 and verify that the new equation is exact.
4. If the new DE is written in the form M(x, y) dx + N(x, y) dy = 0, one has:
My =
Nx = =
Since My and Nx equal, the equation is exact.