What is the solution for (d^2x)/(dt^2)+4(dx)/(dt)+4x=3sin(2t) ?

The solution for (d^2x)/(dt^2)+4(dx)/(dt)+4x=3sin(2t) is x=c_{1}e^{-2t}+c_{2}te^{-2t}-3/8 cos(2t)

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(d^2x)/(dt^2)+4(dx)/(dt)+4x=3sin(2t)

\frac{d ^{2} x}{d t ^{2}} + 4 \frac{d x}{d t} + 4 x = 3 sin (2 t)

x = c_{1} e^{- 2 t} + c_{2} t e^{- 2 t} - \frac{3}{8} cos (2 t)

Solution steps

\frac{d ^{2} x}{d t ^{2}} + 4 \frac{d x}{d t} + 4 x = 3 sin (2 t)

Solve linear ODE:

x = c_{1} e^{- 2 t} + c_{2} t e^{- 2 t} - \frac{3}{8} cos (2 t)

x = c_{1} e^{- 2 t} + c_{2} t e^{- 2 t} - \frac{3}{8} cos (2 t)

y^{^{''}} + 4 y = cos (x), y (π) = 0, y (0) = 0

x^{^{''}} - 10 x^{^{'}} + 25 x = 4 t e^{5 t}

x^{^{''}} + 9 x = 2 sin (t)

y^{^{''}} + 2 y^{^{'}} = 2

y^{^{''}} + 2 y^{^{'}} = 7

What is the solution for (d^2x)/(dt^2)+4(dx)/(dt)+4x=3sin(2t) ?
The solution for (d^2x)/(dt^2)+4(dx)/(dt)+4x=3sin(2t) is x=c_{1}e^{-2t}+c_{2}te^{-2t}-3/8 cos(2t)