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

The solution for (d^2x)/(dt^2)+9x=e^t+sin(t) is x=c_{1}cos(3t)+c_{2}sin(3t)+1/10 e^t+1/8 sin(t)

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

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

x = c_{1} cos (3 t) + c_{2} sin (3 t) + \frac{1}{10} e^{t} + \frac{1}{8} sin (t)

Solution steps

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

Solve linear ODE:

x = c_{1} cos (3 t) + c_{2} sin (3 t) + \frac{1}{10} e^{t} + \frac{1}{8} sin (t)

x = c_{1} cos (3 t) + c_{2} sin (3 t) + \frac{1}{10} e^{t} + \frac{1}{8} sin (t)

What is the solution for (d^2x)/(dt^2)+9x=e^t+sin(t) ?
The solution for (d^2x)/(dt^2)+9x=e^t+sin(t) is x=c_{1}cos(3t)+c_{2}sin(3t)+1/10 e^t+1/8 sin(t)