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

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

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(d^2x)/(dt^2)+2(dx)/(dt)+2x=2

\frac{d ^{2} x}{d t ^{2}} + 2 \frac{d x}{d t} + 2 x = 2

x = e^{- t} (c_{1} cos (t) + c_{2} sin (t)) + 1

Solution steps

\frac{d ^{2} x}{d t ^{2}} + 2 \frac{d x}{d t} + 2 x = 2

Solve linear ODE:

x = e^{- t} (c_{1} cos (t) + c_{2} sin (t)) + 1

x = e^{- t} (c_{1} cos (t) + c_{2} sin (t)) + 1

\frac{d ^{2} y}{d x ^{2}} + \frac{d y}{d x} - y = x sinh (x)

y^{^{''}} + y = sin (x)

y^{^{'''}} + 12 y^{^{''}} + 48 y^{^{'}} + 64 y = 4 e^{- 4 x}

(D^{2} + 9) y = cos^{2} (x)

x y^{^{''}} + x y^{^{'}} = x^{3}

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