Chapter 1.2, Problem 44P

The differential equation $y^{″}+y=0$ has the general solution $y\left(x\right)=c_1\cos x+c_2\sin x$.

(a) Show that the boundary-value problem $y^{″}+y=0$, $y\left(\pi \right)=1$ has no solutions.

(b) Show that the boundary-value problem $y^{″}+y=0$, $y\left(0\right)=0$, $y\left(\pi \right)=0$ has an infinite number of solutions.