Show that, if we change the independent variables (x,y) to (s,t), where $\displaystyle x = e^s cos t$ and $\displaystyle y = e^s sin t$, then

$\displaystyle \frac{\partial^2 u}{\partial s^2} + \frac{\partial^2 u}{\partial t^2} = (x^2 + y^2)(\frac{\partial^2 u}{\partial x^2} + \frac{\partial^2 u}{\partial y^2})$

Now... Whats u? do you not need u to be equal to some function of x and y to be able to solve this?