Solve by using D'Alembert's solution with the even extensions of f(x) and g(x)
where
, where
where
Since we have the boundary condition we would consider even extensions. Let be even extensions, and we will also assume that these extensions are well-behaved to satisfy the condition of D'Alembert's solution. Thus, we have that for . Thus, the solution is given by:
.
Notice that therefore , this is precisely what we want.