What is the solution for (d^2x)/(dt^2)+36x=10sin(4t) ?

The solution for (d^2x)/(dt^2)+36x=10sin(4t) is x=c_{1}cos(6t)+c_{2}sin(6t)+1/2 sin(4t)

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(d^2x)/(dt^2)+36x=10sin(4t)

\frac{d ^{2} x}{d t ^{2}} + 36 x = 10 sin (4 t)

x = c_{1} cos (6 t) + c_{2} sin (6 t) + \frac{1}{2} sin (4 t)

Solution steps

\frac{d ^{2} x}{d t ^{2}} + 36 x = 10 sin (4 t)

Solve linear ODE:

x = c_{1} cos (6 t) + c_{2} sin (6 t) + \frac{1}{2} sin (4 t)

x = c_{1} cos (6 t) + c_{2} sin (6 t) + \frac{1}{2} sin (4 t)

What is the solution for (d^2x)/(dt^2)+36x=10sin(4t) ?
The solution for (d^2x)/(dt^2)+36x=10sin(4t) is x=c_{1}cos(6t)+c_{2}sin(6t)+1/2 sin(4t)