Find a solution of an initial value problem by introducing an
appropriate substitution (compare Problems 37 and 38). You
don't need to write your solution in terms of the error function.
Prove that a given total energy is conserved.
Find the Fourier series of a given (and easy) function.
Find a solution of a partial difference equation by separating
the variables. You may use the results of Problem 46 for the
solution of this problem.