What is the solution for linear (d^2x)/(dt^2)+x=6cos(2t) ?

The solution for linear (d^2x)/(dt^2)+x=6cos(2t) is x=c_{1}cos(t)+c_{2}sin(t)-2cos(2t)

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linear (d^2x)/(dt^2)+x=6cos(2t)

linear

\frac{d ^{2} x}{d t ^{2}} + x = 6 cos (2 t)

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

Solution steps

\frac{d ^{2} x}{d t ^{2}} + x = 6 cos (2 t)

Solve linear ODE:

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

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

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

y^{^{''}} + 4 y^{^{'}} + 4 y = 4 x^{2} - 8 x

y^{^{''}} + y = (sec (x))^{3}

y^{^{''}} - 2 y^{^{'}} - 3 y = 3 x e^{2 x}, y (0) = 1, y^{^{'}} (0) = 0

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

What is the solution for linear (d^2x)/(dt^2)+x=6cos(2t) ?
The solution for linear (d^2x)/(dt^2)+x=6cos(2t) is x=c_{1}cos(t)+c_{2}sin(t)-2cos(2t)