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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

y^{^{''}} - 2 y^{^{'}} - 3 y = 3 \cdot e^{- t}

y^{^{''}} - y^{^{'}} - a^{2} = 0

y^{^{''}} + 6 y^{^{'}} + 9 y = t + e^{3 t}

y^{^{''}} + 16 y = 5 cos (4 t), y (0) = 1, y^{^{'}} (0) = 0

y^{^{''}} - 9 y = 4, y^{1} (0) = e^{- 3 x}

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