What is the solution for x^2y^{''}-2y^'=0 ?

The solution for x^2y^{''}-2y^'=0 is y=e^{-2/x+c_{1}}x+2e^{c_{1}}\Ei(-2/x)+c_{2}

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x^2y^{''}-2y^'=0

x^{2} y^{^{''}} - 2 y^{^{'}} = 0

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

Solution steps

x^{2} y^{''} (x) - 2 y^{'} (x) = 0

Solve using substitution:

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

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

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What is the solution for x^2y^{''}-2y^'=0 ?
The solution for x^2y^{''}-2y^'=0 is y=e^{-2/x+c_{1}}x+2e^{c_{1}}\Ei(-2/x)+c_{2}