Consider this second-order nonhomogeneous differential equation:
$Consider this second-order nonhomogeneous differential equation: Which of the following is the form of the solution of the corresponding homogeneous differential equation? Here, C1 and C2 are arbitrary real constants. A) y(t) =C_{1} e^{5 t}(\sin (-5 t) +\cos (-5 t) ) +C_{2} B) y(t) =C_{1} e^{-5 t} \sin (5 t) +C_{2} e^{-5 t} \cos (5 t) C) y(t) =C_{1} e^{5 t} \sin (-5 t) +C_{2} e^{5 t} \cos (-5 t) D) y(t) =C_{1} e^{-5 t}(\sin (5 t) +\cos (5 t) ) +C_{2}$
Which of the following is the form of the solution of the corresponding homogeneous differential equation? Here, C₁ and C₂ are arbitrary real constants.

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The Answer of Consider this second-order nonhomogeneous differential equation: Which of the following is the form of the solution of the corresponding homogeneous differential equation? Here, C₁ and C₂ are arbitrary real constants. A) $ y(t)=C_{1} e^{5 t}(\sin (-5 t)+\cos (-5 t))+C_{2} $ B) $ y(t)=C_{1} e^{-5 t} \sin (5 t)+C_{2} e^{-5 t} \cos (5 t) $ C) $ y(t)=C_{1} e^{5 t} \sin (-5 t)+C_{2} e^{5 t} \cos (-5 t) $ D) $ y(t)=C_{1} e^{-5 t}(\sin (5 t)+\cos (5 t))+C_{2} $

Consider This Second-Order Nonhomogeneous Differential Equation: Which of the Following

Consider This Second-Order Nonhomogeneous Differential Equation:

Which of the Following