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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.

  1. No solution.
  2. Exactly two solutions.
  3. Exactly one solution.
  4. Infinitely many solutions. 
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