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

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

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

(d^{3} - d) \cdot y = x^{3}

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

Solution steps

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

Solve linear ODE:

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

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

(d^{2} - 1) y = x

(d^{2} + 2) y = x^{2} e^{3} x

y^{^{''}} - 4 y^{^{'}} + 4 y = (x + 1) e^{2} x

(d^{2} - 4 d - 12) \cdot y = (x - 1) \cdot e^{- 2 x}

(d^{2} + 4 d + 4) y = x^{2} + e^{x} + cos (x)

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