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) $

Question

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) $

Quizplus · Accepted Answer

The Answer of 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) $