Translate the following into a PDE with boundary conditions.

The left end of a rod of length $L$ is held at temperature $20$, and the right end is held at temperature $57$. The initial temperature of the rod is 0 throughout. How to enter the answers.

The PDE is
The boundary values / initial conditions are:
Left end is held at temperature $20$:
Right end is held at temperature $57$:
Initial temperature is 0: