Use variation of parameters to find the general solution of the nonhomogeneous differential equation
A) $ \left.y(t)=C_{1} \cos (5 t)+C_{2} \sin (5 t)+\frac{1}{25} \cos ^{2}(5 t)-\frac{1}{75} \cos ^{4} 5 t\right)+\frac{1}{75} \sin ^{4}(5 t) $
B) $ y(t)=C_{1} \cos (5 t)+C_{2} \sin (5 t)+\cos ^{2}(5 t)-\frac{1}{3} \cos ^{4}(5 t)+\frac{1}{3} \sin ^{4}(5 t) $
C) $ y(t)=C_{1} \cos (5 t)+C_{2} \sin (5 t)+\frac{1}{5} \sin (5 t) \cos (5 t)\left[1-\frac{1}{3} \cos ^{2}(5 t)\right]+\frac{1}{15} \sin ^{3}(5 t) \cos (5 t) $
D) $ y(t)=C_{1} \cos (5 t)+C_{2} \sin (5 t)+\sin (5 t) \cos (5 t)\left[1-\frac{1}{3} \cos ^{2}(5 t)\right)+\frac{1}{3} \sin ^{3}(5 t) \cos (5 t) $

Question

Use variation of parameters to find the general solution of the nonhomogeneous differential equation  
A) $ \left.y(t)=C_{1} \cos (5 t)+C_{2} \sin (5 t)+\frac{1}{25} \cos ^{2}(5 t)-\frac{1}{75} \cos ^{4} 5 t\right)+\frac{1}{75} \sin ^{4}(5 t) $ 
B) $ y(t)=C_{1} \cos (5 t)+C_{2} \sin (5 t)+\cos ^{2}(5 t)-\frac{1}{3} \cos ^{4}(5 t)+\frac{1}{3} \sin ^{4}(5 t) $ 
C) $ y(t)=C_{1} \cos (5 t)+C_{2} \sin (5 t)+\frac{1}{5} \sin (5 t) \cos (5 t)\left[1-\frac{1}{3} \cos ^{2}(5 t)\right]+\frac{1}{15} \sin ^{3}(5 t) \cos (5 t) $ 
D) $ y(t)=C_{1} \cos (5 t)+C_{2} \sin (5 t)+\sin (5 t) \cos (5 t)\left[1-\frac{1}{3} \cos ^{2}(5 t)\right)+\frac{1}{3} \sin ^{3}(5 t) \cos (5 t) $

Quizplus · Accepted Answer

The Answer of Use variation of parameters to find the general solution of the nonhomogeneous differential equation  
A) $ \left.y(t)=C_{1} \cos (5 t)+C_{2} \sin (5 t)+\frac{1}{25} \cos ^{2}(5 t)-\frac{1}{75} \cos ^{4} 5 t\right)+\frac{1}{75} \sin ^{4}(5 t) $ 
B) $ y(t)=C_{1} \cos (5 t)+C_{2} \sin (5 t)+\cos ^{2}(5 t)-\frac{1}{3} \cos ^{4}(5 t)+\frac{1}{3} \sin ^{4}(5 t) $ 
C) $ y(t)=C_{1} \cos (5 t)+C_{2} \sin (5 t)+\frac{1}{5} \sin (5 t) \cos (5 t)\left[1-\frac{1}{3} \cos ^{2}(5 t)\right]+\frac{1}{15} \sin ^{3}(5 t) \cos (5 t) $ 
D) $ y(t)=C_{1} \cos (5 t)+C_{2} \sin (5 t)+\sin (5 t) \cos (5 t)\left[1-\frac{1}{3} \cos ^{2}(5 t)\right)+\frac{1}{3} \sin ^{3}(5 t) \cos (5 t) $

Use Variation of Parameters to Find the General Solution of the Nonhomogeneous