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

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