Translate the following into a PDE with boundary conditions.

The ends of a horizontal string of length L are secured at both ends. The string is initially undisplaced but it has initial vertical velocity $\sin\!\left(\frac{\pi x}{L}\right)$. How to enter the answers.

The PDE is
The boundary values / initial conditions are:
Left end is secured:
Right end is secured:
Initially undisplaced:
Initial velocity is $\sin\!\left(\frac{\pi x}{L}\right)$: