What is the solution for linear (d^2x)/(dt^2)+x=6cos(2t),x(0)=3 ?

The solution for linear (d^2x)/(dt^2)+x=6cos(2t),x(0)=3 is x=5cos(t)+c_{2}sin(t)-2cos(2t)

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linear (d^2x)/(dt^2)+x=6cos(2t),x(0)=3

linear

\frac{d ^{2} x}{d t ^{2}} + x = 6 cos (2 t), x (0) = 3

x = 5 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 = 5 cos (t) + c_{2} sin (t) - 2 cos (2 t)

x = 5 cos (t) + c_{2} sin (t) - 2 cos (2 t)

What is the solution for linear (d^2x)/(dt^2)+x=6cos(2t),x(0)=3 ?
The solution for linear (d^2x)/(dt^2)+x=6cos(2t),x(0)=3 is x=5cos(t)+c_{2}sin(t)-2cos(2t)