Question

I notice there are alot of algebra questions today. If you're bored and feel like solving a fourth order PDE for no reason, try this:

Solve the cantilever-beam problem:

\[\frac{∂^2u}{∂t^2}+\frac{∂^4u}{∂x^4}=0\]\[0 < x < 1\]\[0 < t < \infty\]
Boundary Conditions:\[\left(\begin{matrix}u(0,t)=0\\u_x(0,t)=0\\u_{xx}(1,t)=0 \\ u_{xxx}(1,t)=0\end{matrix}\right)0 < t < \infty\]
Initial Conditions:\[\left(\begin{matrix}u(x,0)=f(x) \\ u_t(x,0)=g(x)\end{matrix}\right) 0 \le x \le 1\]