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 held motionless with initial vertical displacement $x\!\left(L-x\right)$, then released. How to enter the answers.

The PDE is
The boundary values / initial conditions are:
Left end is secured:
Right end is secured:
Released from rest:
Initial displacement is $x\!\left(L-x\right)$: