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Which of These Is the General Solution of the Second-Order y(t)=C1+C2e65t+At+B+(Ct+D)e65t y(t)=C_{1}+C_{2} e^{-\frac{6}{5} t}+A t+B+(C t+D) e^{-\frac{6}{5} t}

Question 85

Multiple Choice

Which of these is the general solution of the second-order nonhomogeneous differential equation  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}+C_{2} e^{-\frac{6}{5} t}+A t+B+(C t+D)  e^{-\frac{6}{5} t}   B)    y(t) =C_{1}+C_{2} e^{\frac{6}{5} t}+A t^{2}+B t+C+\left(D t^{2}+E t+F\right)  e^{-\frac{6}{5} t}   C)    y(t) =C_{1}+C_{2} e^{\frac{6}{5} t}+t^{2}\left(A+B e^{-\frac{6}{5} t}\right)    D)    y(t) =C_{1}+C_{2} e^{-\frac{6}{5} t}+A t^{2}+B t+C+\left(D t^{2}+E t+F\right)  e^{-\frac{6}{5} t}   E)    y(t) =C_{1}+C_{2} e^{-\frac{6}{5} t}+t^{2}\left(A+B e^{-\frac{6}{5} t}\right)
and all capital letters are arbitrary real constants.


A) y(t) =C1+C2e65t+At+B+(Ct+D) e65t y(t) =C_{1}+C_{2} e^{-\frac{6}{5} t}+A t+B+(C t+D) e^{-\frac{6}{5} t}
B) y(t) =C1+C2e65t+At2+Bt+C+(Dt2+Et+F) e65t y(t) =C_{1}+C_{2} e^{\frac{6}{5} t}+A t^{2}+B t+C+\left(D t^{2}+E t+F\right) e^{-\frac{6}{5} t}
C) y(t) =C1+C2e65t+t2(A+Be65t) y(t) =C_{1}+C_{2} e^{\frac{6}{5} t}+t^{2}\left(A+B e^{-\frac{6}{5} t}\right)
D) y(t) =C1+C2e65t+At2+Bt+C+(Dt2+Et+F) e65t y(t) =C_{1}+C_{2} e^{-\frac{6}{5} t}+A t^{2}+B t+C+\left(D t^{2}+E t+F\right) e^{-\frac{6}{5} t}
E) y(t) =C1+C2e65t+t2(A+Be65t) y(t) =C_{1}+C_{2} e^{-\frac{6}{5} t}+t^{2}\left(A+B e^{-\frac{6}{5} t}\right)

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