To prove using Euler theorem, partial differntiation

Question

If $$u=\tan^{-1}(\frac{x^3+y^3}{2x+3y})$$ then prove that $$x^2\frac{\partial^2u}{\partial x^2}+2xy\frac{\partial^2 u}{\partial x\partial y }+y^2\frac{\partial^2u}{\partial y^2}=(1-4\sin^2 u)sin 2u$$