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What Is the Form of a Particular Solution of the Following

Question 54

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What is the form of a particular solution of the following nonhomogeneous differential equation?
 What is the form of a particular solution of the following nonhomogeneous differential equation?   All capital letters in the choices represent arbitrary real constants. A)    A e^{-5 t}   B)    (A t+B)  e^{-5 t}   C)    \left(A t^{2}+B t+C\right)  e^{-5 t}   D)    \left(A t^{3}+B t^{2}+C t+D\right)  e^{-5 t}
All capital letters in the choices represent arbitrary real constants.


A) Ae5t A e^{-5 t}
B) (At+B) e5t (A t+B) e^{-5 t}
C) (At2+Bt+C) e5t \left(A t^{2}+B t+C\right) e^{-5 t}
D) (At3+Bt2+Ct+D) e5t \left(A t^{3}+B t^{2}+C t+D\right) e^{-5 t}

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