What is the solution for (d^2x)/(dt^2)+7(dx)/(dt)+6x=5e^{-t} ?

The solution for (d^2x)/(dt^2)+7(dx)/(dt)+6x=5e^{-t} is x=c_{1}e^{-t}+c_{2}e^{-6t}+e^{-t}t

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(d^2x)/(dt^2)+7(dx)/(dt)+6x=5e^{-t}

\frac{d ^{2} x}{d t ^{2}} + 7 \frac{d x}{d t} + 6 x = 5 e^{- t}

x = c_{1} e^{- t} + c_{2} e^{- 6 t} + e^{- t} t

Solution steps

\frac{d ^{2} x}{d t ^{2}} + 7 \frac{d x}{d t} + 6 x = 5 e^{- t}

Solve linear ODE:

x = c_{1} e^{- t} + c_{2} e^{- 6 t} + e^{- t} t

x = c_{1} e^{- t} + c_{2} e^{- 6 t} + e^{- t} t

y^{^{''}} + 2 y^{^{'}} + 5 = 2 cos (t + 0.523599)

y^{^{''}} + 4 y = cos (2 t), y (0) = 1, y^{^{'}} (0) = 1

\frac{d ^{2} x}{d t ^{2}} + 2 \frac{d x}{d t} + x = 3 cos (t)

y^{^{''}} - 18 y = tan (x)

8 y^{^{''}} + 0.25 y^{^{'}} + 512 y = 2 cos (2 t)

What is the solution for (d^2x)/(dt^2)+7(dx)/(dt)+6x=5e^{-t} ?
The solution for (d^2x)/(dt^2)+7(dx)/(dt)+6x=5e^{-t} is x=c_{1}e^{-t}+c_{2}e^{-6t}+e^{-t}t