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

(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: \[ \begin{aligned} y(0) & =1 \\ \psi\left(\frac{3 \pi}{4}\right) & =-1 \end{aligned} \] \[ y= \] -B) Boundary conditions: \[ \begin{aligned} y(0) & =1 \\ y\left(\frac{5 \pi}{2}\right) & =-1 \end{aligned} \] \[ y= \] - C) Boundary conditions: \[ \begin{array}{r} y(0)=1 \\ y\left(\frac{15 \pi}{8}\right)=-1 \end{array} \] \[ y= \]