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

The solution for d/(dt)((dx)/(dt))+x=sin(2t) is x=c_{1}cos(t)+c_{2}sin(t)-1/3 sin(2t)

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d/(dt)((dx)/(dt))+x=sin(2t)

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

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

Solution steps

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

Solve linear ODE:

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

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

\int_{0}^{\infty} 8 sin^{2} (a) d a

y^{^{''}} - 10 y^{^{'}} + 25 y = e^{5 x}

\int_{0}^{2} 144 x + 289 d x

16 4 4 x^{4} + 4

t^{3} - \frac{1}{4 t ^{7}}

What is the solution for d/(dt)((dx)/(dt))+x=sin(2t) ?
The solution for d/(dt)((dx)/(dt))+x=sin(2t) is x=c_{1}cos(t)+c_{2}sin(t)-1/3 sin(2t)