homogeneous partial differential equation Is $$z\frac{\partial z}{\partial x} + x^2\frac{\partial z}{\partial y} = y^2$$ equation homogeneous partial differential equation? Why??
$$z\frac{\partial z}{\partial x} + x^2\frac{\partial z}{\partial y} = y^2$$
$$\implies \frac{\partial z}{\partial x} + \frac{x^2}{z}\frac{\partial z}{\partial y} = \frac{y^2}{z}$$
Is it because this PDE has $z$ or its partial derivative in each term?  

The differential equation given is not homogeneous. 
The reason is quite simple, it is because $z(x,y)=0$ is not a solution to the PDE.
