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

The solution for y^{''}-2y^'+y=(e^{-x})/x is y=c_{1}e^x+c_{2}xe^x+1/2 e^{-x}+e^xx\Ei(-2x)

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

y^{^{''}} - 2 y^{^{'}} + y = \frac{e ^{- x}}{x}

y = c_{1} e^{x} + c_{2} x e^{x} + \frac{1}{2} e^{- x} + e^{x} x Ei (- 2 x)

Solution steps

y^{''} (x) - 2 y^{'} (x) + y = \frac{e ^{- x}}{x}

Solve linear ODE:

y = c_{1} e^{x} + c_{2} x e^{x} + \frac{1}{2} e^{- x} + e^{x} x Ei (- 2 x)

y = c_{1} e^{x} + c_{2} x e^{x} + \frac{1}{2} e^{- x} + e^{x} x Ei (- 2 x)

x^{^{''}} + 16 x = 36 cos (2 t)

y^{^{''}} - 12 y^{^{'}} + 36 y = 7 e^{6 x}

y^{^{''}} + \frac{1}{8} y^{^{'}} + y = 3 cos (t)

y^{^{''}} + 9 y^{^{'}} + 14 y = \frac{1}{2} sin (t)

(D^{2} - 4 D + 4) (y) = 6 x^{2} e^{2 x}

What is the solution for y^{''}-2y^'+y=(e^{-x})/x ?
The solution for y^{''}-2y^'+y=(e^{-x})/x is y=c_{1}e^x+c_{2}xe^x+1/2 e^{-x}+e^xx\Ei(-2x)