What is the solution for x^{''}+9x=8sin(3t) ?

The solution for x^{''}+9x=8sin(3t) is x=c_{1}cos(3t)+c_{2}sin(3t)-(4tcos(3t))/3

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x^{''}+9x=8sin(3t)

x^{^{''}} + 9 x = 8 sin (3 t)

x = c_{1} cos (3 t) + c_{2} sin (3 t) - \frac{4 t cos ( 3 t )}{3}

Solution steps

x^{''} (t) + 9 x = 8 sin (3 t)

Solve linear ODE:

x = c_{1} cos (3 t) + c_{2} sin (3 t) - \frac{4 t cos ( 3 t )}{3}

x = c_{1} cos (3 t) + c_{2} sin (3 t) - \frac{4 t cos ( 3 t )}{3}

\frac{d ^{2} y}{d x ^{2}} - 4 y = 10 e^{3 x}

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

\frac{d ^{2} y}{d x ^{2}} - \frac{d y}{d x} + y = x^{3} + 6

y^{^{''}} + 8 y^{^{'}} + 17 y = 17 x^{2} - x + 28

\frac{d ^{2} y}{d x ^{2}} + 4 \frac{d y}{d x} + 3 y = e^{- 2 x}

What is the solution for x^{''}+9x=8sin(3t) ?
The solution for x^{''}+9x=8sin(3t) is x=c_{1}cos(3t)+c_{2}sin(3t)-(4tcos(3t))/3