(Solved): Consider the differential equation \[ y^{\prime \prime}+2 y^{\prime}-15 y=-8500 \cos (5 x) \text {. ...

Consider the differential equation \[ y^{\prime \prime}+2 y^{\prime}-15 y=-8500 \cos (5 x) \text {. } \] Use coefficients \( c_{1} \) and \( c_{2} \) if needed. (a) find the general solution of the homogeneous equation: \[ y_{h}(x)= \] (b) find a particular solution to the nonhomogeneous equation using the method of undetermined coefficients: \[ y_{p}(x)= \] (c) find the general solution to the nonhomogeneous equation: \( y(x) \)