What is the solution for (d^2y)/(dx^2)-y= 1/x ?

The solution for (d^2y)/(dx^2)-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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(d^2y)/(dx^2)-y= 1/x

\frac{d ^{2} y}{d x ^{2}} - 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

\frac{d ^{2} y}{d x ^{2}} - 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}

6 y^{^{''}} - y^{^{'}} - 2 y = 3 sin (10) x

d, d (x) = \frac{3 x - 2}{x + 1}

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

\frac{d ^{2} y}{d x ^{2}} - 6 \frac{d y}{d x} = 37 sin (x)

y^{^{''}} - 7 y^{^{'}} + 10 y = e^{x}

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