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

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

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

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

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

Solution steps

(d + 1)^{3} y = 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 ^{3}}{3}

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

(d^{2} - 3 d + 2) \cdot y = 3 sin (x)

y^{^{'''}} - y^{^{''}} - 4 y^{^{'}} + 4 y = 5 - e^{x} + e^{2} x

y^{^{'''}} - 4 y^{^{'}} = 0

y^{^{'''}} - 4 y = 0

2 y^{^{''}} - 3 y^{^{'}} + y = 0, y (0) = 0, y^{^{'}} (0) = 1

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