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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

y^{^{''}} + 6 y^{^{'}} + 8 y = e sin (x)

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

(\frac{d ^{2} + 120 d + 1}{10}) y = 12

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

1000 - 0.017 y^{^{'}} = 100 y^{^{''}}

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