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

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

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(d^2y)/(dx^2)+y=sin(2x)

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

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

Solution steps

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

Solve linear ODE:

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

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

y^{^{''}} + 9 y = cos (3 t), y (0) = 2, y^{^{'}} (0) = 5

y^{^{''}} - y^{^{'}} - 6 y = (x^{2} + 3 x) e^{2 x} + cos (2 x)

\frac{d ^{2} y}{d x ^{2}} + \frac{d y}{d x} + 12 y = 20 cos (3 x)

y^{^{''}} + 6 y^{^{'}} + 13 y = e^{- 3 x} \cdot cos (2 x)

y^{^{''}} - y^{^{'}} + y = 6 sin (t) - 3 e^{2 t}

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