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)

y^{^{''}} - 6 y^{^{'}} + 5 y = 3 x + e^{x}, y (0) = 0, y^{^{'}} (0) = 2

y^{^{''}} - y^{^{'}} - 2 y = 2 e^{3 x}

y^{^{''}} + 2 y^{^{'}} + y = 9 - e^{2 x}, y (0) = 0, y^{^{'}} (0) = 1

(3 d^{2} + 3) y = 3 x

y^{^{''}} + 5 y^{^{'}} + 6 y = 4 + 5 x

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)