What is the solution for (d^3-3d-2)y=x^2 ?

The solution for (d^3-3d-2)y=x^2 is y=c_{1}e^{2x}+c_{2}e^{-x}+c_{3}xe^{-x}-(x^2)/2+(3x)/2-9/4

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(d^3-3d-2)y=x^2

(d^{3} - 3 d - 2) y = x^{2}

y = c_{1} e^{2 x} + c_{2} e^{- x} + c_{3} x e^{- x} - \frac{x ^{2}}{2} + \frac{3 x}{2} - \frac{9}{4}

Solution steps

(d^{3} - 3 d - 2) y = x^{2}

Solve linear ODE:

y = c_{1} e^{2 x} + c_{2} e^{- x} + c_{3} x e^{- x} - \frac{x ^{2}}{2} + \frac{3 x}{2} - \frac{9}{4}

y = c_{1} e^{2 x} + c_{2} e^{- x} + c_{3} x e^{- x} - \frac{x ^{2}}{2} + \frac{3 x}{2} - \frac{9}{4}

y^{^{''}} - 3 y^{^{'}} - 4 = - 8 e^{t} cos (2 t)

y^{^{''}} - 64 y = - 192 t + 128 t^{2}

y^{^{'''}} - 5 y^{^{''}} + 6 y^{^{'}} = 2 x + 3 e^{2 x}

y^{^{''}} + 2 y^{^{'}} + 2 y = 2 cos (x) + sin (x)

y^{^{''}} + 2 y^{^{'}} - 3 y = 32 (3 x + 1) e^{- 3 x}

What is the solution for (d^3-3d-2)y=x^2 ?
The solution for (d^3-3d-2)y=x^2 is y=c_{1}e^{2x}+c_{2}e^{-x}+c_{3}xe^{-x}-(x^2)/2+(3x)/2-9/4