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

The solution for (d^2y)/(dx^2)+4y=sin(x) is y=c_{1}cos(2x)+c_{2}sin(2x)+1/3 sin(x)

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

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

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

Solution steps

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

Solve linear ODE:

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

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

y^{^{''}} + 16 y = cos (4 t)

4 y^{^{''}} - y = e^{\frac{x}{2}} + 4

y^{^{''}} + 4 y = 3 csc (2 x)

y^{^{''}} + 4 y^{^{'}} + 4 y = 2 e^{- t}, y (0) = 2, y^{^{'}} (0) = 2

y^{^{''}} + 3 y^{^{'}} + 2 y = \frac{1}{6 + e ^{x}}

What is the solution for (d^2y)/(dx^2)+4y=sin(x) ?
The solution for (d^2y)/(dx^2)+4y=sin(x) is y=c_{1}cos(2x)+c_{2}sin(2x)+1/3 sin(x)