Translate the following into a PDE with boundary conditions.

The left end of a rod of length L is held at temperature 0, and the right end is insulated. The initial temperature is $x^{2}\!\left(x-L\right)$ throughout. How to enter the answers.

The PDE is
The boundary values / initial conditions are:
Left end is held at temperature 0:
Right end is insulated:
Initial temperature is :