The differential equation $\dfrac{d^{2}y}{dx^{2}}+16y=0$ for $y(x)$ with the two boundary conditions $\dfrac{dy}{dx}\bigg \vert _{x=0}=1$ and $\dfrac{dy}{dx}\bigg \vert_{x=\displaystyle \frac{\pi}{2}}=-1$ has.

- No solution.
- Exactly two solutions.
- Exactly one solution.
- Infinitely many solutions.