M(x,y)=2xy³-3y N(x,y)=-3x-αx²y²+2αy ∂M/∂y = 6xy²-3 ∂N/∂x = -3-2αxy² These will be equal and the differential equation will be exact iff: -2α = 6 α = -3 I guess you didn't want to solve the exact differential equation. 2α-α² = 2(-3)-(-3)² = -6-(9) = -15 Edwin