I want to solve the homogenous part of a stretched string problem where $y=y(x)$.
$$y'' + y = 0$$
with the boundary conditions such that: $y(0)=y(\pi/2)=0$
The differential equation gives rise to a solution on the form: $$y = a \cos(x) + b \sin(x)$$
But when applying the boundary conditions I end up with only trivial solution ($a=b=0$).
Have I made a mistake or does these B.C only lead to $a=b=0$?