You can separate this equation using the following assumption:
Meaning that we assume that the solution can be written as the product of two functions X and T, each respectively depending on only x and t. After substituting this in the equation you get:
After dividing by XT and rewriting this becomes:
Because the left and right hand side are only depending on x and t respectively, these must be equal to a constant, say [imath]\alpha[/imath] This gives rise to two ordinary differential equations which can be solved fairly easy. We have for these:
The solution is now:
Can you take it from here to solve the next part of the question?