What is the solution for (d^2x)/(dt^2)+25x=30cos(6t) ?

The solution for (d^2x)/(dt^2)+25x=30cos(6t) is x=c_{1}cos(5t)+c_{2}sin(5t)-30/11 cos(6t)

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(d^2x)/(dt^2)+25x=30cos(6t)

\frac{d ^{2} x}{d t ^{2}} + 25 x = 30 cos (6 t)

x = c_{1} cos (5 t) + c_{2} sin (5 t) - \frac{30}{11} cos (6 t)

Solution steps

\frac{d ^{2} x}{d t ^{2}} + 25 x = 30 cos (6 t)

Solve linear ODE:

x = c_{1} cos (5 t) + c_{2} sin (5 t) - \frac{30}{11} cos (6 t)

x = c_{1} cos (5 t) + c_{2} sin (5 t) - \frac{30}{11} cos (6 t)

What is the solution for (d^2x)/(dt^2)+25x=30cos(6t) ?
The solution for (d^2x)/(dt^2)+25x=30cos(6t) is x=c_{1}cos(5t)+c_{2}sin(5t)-30/11 cos(6t)