So this is NOT "solving" a differential equation, it is creating a differential equation.
The derivative of a constant is 0 so start differentiating!
Differentiate with respect to x
\(\displaystyle 2z\frac{\partial z}{\partial x}= 3ax^2\)
Differentiate again with respect to y
\(\displaystyle 2z\frac{\partial^2z}{\partial x\partial y}+ 2\frac{\partial z}{\partial x}\frac{\partial z}{\partial y}= 0\)
