What is the solution for (d^2x)/(dt^2)+4(dx)/(dt)+4x=7-2t^2 ?

The solution for (d^2x)/(dt^2)+4(dx)/(dt)+4x=7-2t^2 is x=c_{1}e^{-2t}+c_{2}te^{-2t}-(t^2)/2+t+1

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(d^2x)/(dt^2)+4(dx)/(dt)+4x=7-2t^2

\frac{d ^{2} x}{d t ^{2}} + 4 \frac{d x}{d t} + 4 x = 7 - 2 t^{2}

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

Solution steps

\frac{d ^{2} x}{d t ^{2}} + 4 \frac{d x}{d t} + 4 x = 7 - 2 t^{2}

Solve linear ODE:

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

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

y^{^{''}} + 4 y = sin (3 t)

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

y^{^{''}} + 2 y^{^{'}} + 5 y = 1 + e^{x}

y^{^{''}} + 4 y = sin (t) H (t - 2 π)

y^{^{''}} - 6 y^{^{'}} + 9 y = \frac{( e ^{3 x} )}{x ^{2}}

What is the solution for (d^2x)/(dt^2)+4(dx)/(dt)+4x=7-2t^2 ?
The solution for (d^2x)/(dt^2)+4(dx)/(dt)+4x=7-2t^2 is x=c_{1}e^{-2t}+c_{2}te^{-2t}-(t^2)/2+t+1