For the equation
$\frac{\partial^2}{{\partial}x^2}(IE\frac{{\partial^2}u}{{\partial}x^2}) = \mu(\frac{{\partial^2}u}{{\partial}t^2})$
with $E$ a function of x, derive two ODE's by separation of variables.
I greatly appreciate your help/advice. I'm pretty unsure with how to handle derivatives like this. This is my best attempt, I've been working on this one for quite a while.