What is the solution for (d^2x)/(dt^2)+100x=1000sin(2t) ?

The solution for (d^2x)/(dt^2)+100x=1000sin(2t) is x=c_{1}cos(10t)+c_{2}sin(10t)+125/12 sin(2t)

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(d^2x)/(dt^2)+100x=1000sin(2t)

\frac{d ^{2} x}{d t ^{2}} + 100 x = 1000 sin (2 t)

x = c_{1} cos (10 t) + c_{2} sin (10 t) + \frac{125}{12} sin (2 t)

Solution steps

\frac{d ^{2} x}{d t ^{2}} + 100 x = 1000 sin (2 t)

Solve linear ODE:

x = c_{1} cos (10 t) + c_{2} sin (10 t) + \frac{125}{12} sin (2 t)

x = c_{1} cos (10 t) + c_{2} sin (10 t) + \frac{125}{12} sin (2 t)

y^{^{''}} - 6 y^{^{'}} + 8 y = x^{2} - 5 x

y^{^{''}} - y^{^{'}} + y = 17 sin (t)

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

3 x^{^{''}} + 3 x = 5 cos (4 t)

y^{^{''}} + \frac{1}{8} y^{^{'}} + y = 3 \cdot cos (x)

What is the solution for (d^2x)/(dt^2)+100x=1000sin(2t) ?
The solution for (d^2x)/(dt^2)+100x=1000sin(2t) is x=c_{1}cos(10t)+c_{2}sin(10t)+125/12 sin(2t)