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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

4 y^{^{''}} - 4 y^{^{'}} - 8 y = 8 e^{- t}

y^{^{'''}} - 4 y^{^{'}} = t e^{- 2 t} + 3 cos (2 t)

y^{^{''}} + 49 y = 4 cos (7 x) + 6 sin (7 x)

y^{^{''}} + y^{^{'}} = - 8 e^{- x} - 4

x^{^{''}} + 2 x^{^{'}} + 5 x = 12 cos (2 t) + 3 sin (2 t)

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