In this case, we have , and the general solution is of the form .

The condition implies that , and the condition implies that .

We can instruct Maple to verify this reasoning as follows:

> H:='H';de1 := diff(H(x),x$2)=omega^2*H(x);

> sol1 := dsolve(de1,H(x));

> H:=unapply(rhs(sol1),x);

> solve({D(H)(0)=0,H(Pi)=0},{_C1,_C2});