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

Multiple Choice

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) $y(t) =C_{1} \cos (5 t) +C_{2} \sin (5 t) +\sin (5 t) \cos (5 t) \left[1-\frac{1}{3} \cos ^{2}(5 t) \right) +\frac{1}{3} \sin ^{3}(5 t) \cos (5 t)$