(Solved): 20 points) Solve the following differential equation with the given boundary conditions. - If ther ...

20 points) Solve the following differential equation with the given boundary conditions. - If there are infinitely many solutions, use \( \mathbf{c} \) for any undetermined constants. - If there are no solutions, write No Solution. - Write answers as functions of \( x \) (i.e. \( y=y(x) \) ). \[ y^{\prime \prime}+16 y=0 \] - A) Boundary conditions: \( \quad y(0)=2 \) \[ y\left(\frac{9 \pi}{4}\right)=-2 \] \[ y= \] B) Boundary conditions: \[ \begin{aligned} y(0) & =2 \\ y\left(\frac{\pi}{8}\right) & =-2 \end{aligned} \] \[ y= \] - C) Boundary conditions: \[ \begin{aligned} y(0) & =2 \\ y\left(\frac{\pi}{4}\right) & =2 \end{aligned} \] \[ y= \]