Hi guys i need to help with this excercises. :)

> 
> If 
>  $$\begin{cases}
> x=r\cos \theta\\
> y=r \sin\theta
> \end{cases}$$
>  prove that the equation:
>  $$x^2\frac{\partial^2z}{\partial x^2}+2xy\frac{\partial^2z}{\partial x\partial y}+y^2\frac{\partial^2z}{\partial y^2}=0$$
>  is equivalent to 
>  $$r^2\frac{\partial^2z}{\partial \theta^2}=0.$$
> 
> 
> OK I´VE TRIED
> 
> 
> 

this could be helpful ? then, what do i make?

I tried of isolate $\frac{\partial z}{\partial x}$ and $\frac{\partial z}{\partial y}$

$$\frac{\partial z}{\partial x}=\frac{\partial z}{\partial r}cos\theta-\frac{\partial z}{\partial \theta}(\frac{1}{r})sin\theta$$and
$$\frac{\partial z}{\partial y}=\frac{\partial z}{\partial \theta}(\frac{1}{r})cos\theta+\frac{\partial z}{\partial r}sin\theta$$

mm and we know that
$$\frac{\partial z}{\partial r}=\frac{\partial z}{\partial x}cos\theta+\frac{\partial z}{\partial y}sin\theta$$
$$\frac{\partial z}{\partial \theta}=-\frac{\partial z}{\partial x}rsin\theta+\frac{\partial z}{\partial y}rcos\theta$$

but I do not get anything.

How can I do to get the result??
help.