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

The condition implies that , and the condition implies that or .

This last condition will be true whenever for = 1, 2, 3, ....

We can instruct Maple to verify this reasoning as follows:

> H:='H';de2 := diff(H(x),x$2)=-omega^2*H(x);

> sol2 := dsolve(de2,H(x));

> H:=unapply(rhs(sol2),x);

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

Note that it is up to us to notice that other values of also work.