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

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

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

\frac{d ^{2} y}{d x ^{2}} - y = \frac{1}{x ^{2}}

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

Solution steps

\frac{d ^{2} y}{d x ^{2}} - y = \frac{1}{x ^{2}}

Solve linear ODE:

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

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

y^{^{''}} - 7 y^{^{'}} = 10

(D^{2} - 4) y = 2 cos (2 x)

y^{^{''}} + 9 y = cos (3 t), y (\frac{π}{6}) = 1, y (0) = 1

1.23 \cdot 2 0^{2} π 0.0 2^{2} - 0.017 y^{^{'}} = 0.01 y^{^{''}}

y^{^{''}} - y^{^{'}} - 2 y = 3 e^{(2 x)} - e^{(- x)}

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