What is the solution for (d^2x)/(dt^2)+16x=12cos(9t) ?

The solution for (d^2x)/(dt^2)+16x=12cos(9t) is x=c_{1}cos(4t)+c_{2}sin(4t)-12/65 cos(9t)

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(d^2x)/(dt^2)+16x=12cos(9t)

\frac{d ^{2} x}{d t ^{2}} + 16 x = 12 cos (9 t)

x = c_{1} cos (4 t) + c_{2} sin (4 t) - \frac{12}{65} cos (9 t)

Solution steps

\frac{d ^{2} x}{d t ^{2}} + 16 x = 12 cos (9 t)

Solve linear ODE:

x = c_{1} cos (4 t) + c_{2} sin (4 t) - \frac{12}{65} cos (9 t)

x = c_{1} cos (4 t) + c_{2} sin (4 t) - \frac{12}{65} cos (9 t)

What is the solution for (d^2x)/(dt^2)+16x=12cos(9t) ?
The solution for (d^2x)/(dt^2)+16x=12cos(9t) is x=c_{1}cos(4t)+c_{2}sin(4t)-12/65 cos(9t)