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

The solution for (d+1)^3y=x^2e^{-x} is y=c_{1}e^{-x}+c_{2}xe^{-x}+c_{3}x^2e^{-x}+(e^{-x}x^5)/(60)

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

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

y = c_{1} e^{- x} + c_{2} x e^{- x} + c_{3} x^{2} e^{- x} + \frac{e ^{- x} x ^{5}}{60}

Solution steps

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

Solve linear ODE:

y = c_{1} e^{- x} + c_{2} x e^{- x} + c_{3} x^{2} e^{- x} + \frac{e ^{- x} x ^{5}}{60}

y = c_{1} e^{- x} + c_{2} x e^{- x} + c_{3} x^{2} e^{- x} + \frac{e ^{- x} x ^{5}}{60}

y^{^{''}} + 25 y = cos^{5} (x)

y^{^{'''}} + 3 y^{^{''}} + 3 y^{^{'}} + y = 30 e^{- x}

y^{^{''}} - 6 y^{^{'}} + 9 y = e^{3} x

(d^{2} - 6 d + 9) y = x - 2 e^{3} x

y^{^{''}} + 4 y = 2 tan (x)

What is the solution for (d+1)^3y=x^2e^{-x} ?
The solution for (d+1)^3y=x^2e^{-x} is y=c_{1}e^{-x}+c_{2}xe^{-x}+c_{3}x^2e^{-x}+(e^{-x}x^5)/(60)