What is the solution for (d^3-3d)y=9x^2 ?

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

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(d^3-3d)y=9x^2

(d^{3} - 3 d) y = 9 x^{2}

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

Solution steps

(d^{3} - 3 d) y = 9 x^{2}

Solve linear ODE:

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

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

y^{^{''}} + y^{^{'}} - 12 y = 4 e^{x} sin (2 x) + 4 e^{3 x} + 2

\frac{d ^{2} y}{d x ^{2}} + \frac{d y}{d x} + 2 y = 5 e^{3 x}

\frac{d ^{2} y}{d x ^{2}} + 2 \frac{d y}{d x} - 15 y = (x + 1) e^{x}

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

9 y^{^{''}} - 6 y^{^{'}} + y = 5 - x

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