Which of These Is the General Solution of the Second-Order $y(t)=C_{1} e^{t}+C_{2} t e^{t}+A \sin (\sqrt{7} t)+B \cos (\sqrt{7} t)+C \sin \left(\frac{5 \pi}{2} t\right)+D \cos \left(\frac{5 \pi}{2} t\right)$

Multiple Choice

Which of these is the general solution of the second-order nonhomogeneous differential equation , and all capital letters are arbitrary real constants.

A) $y(t) =C_{1} e^{t}+C_{2} t e^{t}+A \sin (\sqrt{7} t) +B \cos (\sqrt{7} t) +C \sin \left(\frac{5 \pi}{2} t\right) +D \cos \left(\frac{5 \pi}{2} t\right)$
B) $y(t) =C_{1}+C_{2} t+A \sin (\sqrt{7} t) +B \cos (\sqrt{7} t) +C \sin \left(\frac{5 \pi}{2} t\right) +D \cos \left(\frac{5 \pi}{2} t\right)$
C) $y(t) =C_{1}+C_{2} t+A \sin (\sqrt{7} t) +B \cos \left(\frac{5 \pi}{2} t\right)$
D) $y(t) =C_{1} t+A \sin (\sqrt{7} t) +B \cos \left(\frac{5 \pi}{2} t\right)$
E) $y(t) =C_{1} t+A \sin (\sqrt{7} t) +B \cos (\sqrt{7} t) +C \sin \left(\frac{5 \pi}{2} t\right) +D \cos \left(\frac{5 \pi}{2} t\right)$