What is the solution for y^{''}+2y=-4x ?

The solution for y^{''}+2y=-4x is y=c_{1}cos(sqrt(2)x)+c_{2}sin(sqrt(2)x)-2x

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y^{''}+2y=-4x

y^{^{''}} + 2 y = - 4 x

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

Solution steps

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

Solve linear ODE:

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

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

2 e^{- t} cos (4 t)

\frac{d}{d x} (\frac{( 4 x + b )}{( c x + d )})

x y + \frac{d y}{d x} = 100 x

\frac{d y}{d x} + 8 y = e^{x} y^{- 8}

x \to 5 - lim (4 x - 5)

What is the solution for y^{''}+2y=-4x ?
The solution for y^{''}+2y=-4x is y=c_{1}cos(sqrt(2)x)+c_{2}sin(sqrt(2)x)-2x