What is the solution for (d^2x)/(dt^2)+5(dx)/(dt)+4x=e^{6t} ?

The solution for (d^2x)/(dt^2)+5(dx)/(dt)+4x=e^{6t} is x=c_{1}e^{-t}+c_{2}e^{-4t}+1/70 e^{6t}

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(d^2x)/(dt^2)+5(dx)/(dt)+4x=e^{6t}

\frac{d ^{2} x}{d t ^{2}} + 5 \frac{d x}{d t} + 4 x = e^{6 t}

x = c_{1} e^{- t} + c_{2} e^{- 4 t} + \frac{1}{70} e^{6 t}

Solution steps

\frac{d ^{2} x}{d t ^{2}} + 5 \frac{d x}{d t} + 4 x = e^{6 t}

Solve linear ODE:

x = c_{1} e^{- t} + c_{2} e^{- 4 t} + \frac{1}{70} e^{6 t}

x = c_{1} e^{- t} + c_{2} e^{- 4 t} + \frac{1}{70} e^{6 t}

y^{^{''}} - 6 y^{^{'}} + 9 y = 27 e^{6 x}

y^{^{'''}} + 4 y^{^{''}} + 3 y^{^{'}} = 2 + e^{2} t

y^{^{''}} + y^{^{'}} - 2 y = 3 x e^{x}

y^{^{''}} + y = 3 cos (t), y (0) = 0, y^{^{'}} (0) = 0

y^{^{''}} + 6 y^{^{'}} + 5 y = e^{- 3 x}

What is the solution for (d^2x)/(dt^2)+5(dx)/(dt)+4x=e^{6t} ?
The solution for (d^2x)/(dt^2)+5(dx)/(dt)+4x=e^{6t} is x=c_{1}e^{-t}+c_{2}e^{-4t}+1/70 e^{6t}