What is the solution for (d^2y)/(dx^2)+y=3sin(2x) ?

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

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(d^2y)/(dx^2)+y=3sin(2x)

\frac{d ^{2} y}{d x ^{2}} + y = 3 sin (2 x)

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

Solution steps

\frac{d ^{2} y}{d x ^{2}} + y = 3 sin (2 x)

Solve linear ODE:

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

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

y^{^{''}} - 4 y = e^{x} cos (x), y (0) = 0.9, y^{^{'}} (0) = - 1.1

y^{^{''}} - 4 y = e^{- 3 x} sin (e^{- x})

y^{^{''}} - y^{^{'}} - 6 y = 28 cos (3 x)

u^{^{''}} + 3 u^{^{'}} + 5 H (t) = e^{- 5 t}

y^{^{''}} - 4 y^{^{'}} = 3 e^{2 x}, y (0) = 0, y^{^{'}} (0) = 0

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