What is the solution for (d^2y)/(dx^2)+4y=sin(2x) ?

The solution for (d^2y)/(dx^2)+4y=sin(2x) is y=c_{1}cos(2x)+c_{2}sin(2x)-(xcos(2x))/4

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(d^2y)/(dx^2)+4y=sin(2x)

\frac{d ^{2} y}{d x ^{2}} + 4 y = sin (2 x)

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

Solution steps

\frac{d ^{2} y}{d x ^{2}} + 4 y = sin (2 x)

Solve linear ODE:

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

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

\frac{d}{d x} (\frac{- x}{y})

\frac{2}{x + 5}

(- 1, - 4), (5, - 4)

\frac{d}{d x} (4 x - 5 x^{\frac{7}{8}})

f (x) = 8 e^{x} + x, (0, 8)

What is the solution for (d^2y)/(dx^2)+4y=sin(2x) ?
The solution for (d^2y)/(dx^2)+4y=sin(2x) is y=c_{1}cos(2x)+c_{2}sin(2x)-(xcos(2x))/4