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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

y, (d^{3} + d) \cdot y = cos (t) + t^{2} + 3

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

y^{^{''}} + y = 2 t cos (t) cos^{2} (t)

y^{^{''}} - 2 y^{^{'}} - 8 y = 5 e^{2} x

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

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