What is the solution for y^{''}-y= 1/x ?

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

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y^{''}-y= 1/x

y^{^{''}} - y = \frac{1}{x}

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

Solution steps

y^{''} (x) - y = \frac{1}{x}

Solve linear ODE:

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

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

y^{^{'''}} - y^{^{'}} = 4 e^{- x} + 3 e^{2 x}

(d^{2} - 4 d + 3) y = x^{3}

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

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

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

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