What is the solution for (D^2+3D)y=-18x ?

The solution for (D^2+3D)y=-18x is y=c_{1}+c_{2}e^{-3x}-3x^2+2x

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(D^2+3D)y=-18x

(D^{2} + 3 D) y = - 18 x

y = c_{1} + c_{2} e^{- 3 x} - 3 x^{2} + 2 x

Solution steps

(D^{2} + 3 D) y = - 18 x

Solve linear ODE:

y = c_{1} + c_{2} e^{- 3 x} - 3 x^{2} + 2 x

y = c_{1} + c_{2} e^{- 3 x} - 3 x^{2} + 2 x

y^{^{''}} - 2 y^{^{'}} - 8 y = 4 e^{2} - 21 e^{- 3 x}

y^{^{''}} + 3 y^{^{'}} = e^{- 3 t}

(y^{^{''}}) + y = 3 x sin (x)

y^{^{''}} + 500 y^{^{'}} + 20000 y = 1100

y^{^{''}} + 2 y^{^{'}} - 8 y = x + 1

What is the solution for (D^2+3D)y=-18x ?
The solution for (D^2+3D)y=-18x is y=c_{1}+c_{2}e^{-3x}-3x^2+2x