(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 \( c \) 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: \[ \begin{array}{r} y(0)=3 \\ y\left(\frac{9 \pi}{4}\right)=3 \\ y= \end{array} \] - B) Boundary conditions: \[ \begin{array}{l} y(0)=3 \\ y\left(\frac{11 \pi}{8}\right)=-3 \\ y= \end{array} \] - C) Boundary conditions: \[ \begin{aligned} y(0) & =3 \\ y\left(\frac{9 \pi}{4}\right) & =-3 \end{aligned} \]