\[ y''(x)=\frac {2 y'(x)}{(x-2) x}-\frac {y(x)}{(x-2) x^2} \] ✓ Mathematica : cpu = 0.140262 (sec), leaf count = 104
\[\left \{\left \{y(x)\to \left (-\frac {1}{2}\right )^{\frac {1}{\sqrt {2}}} c_2 x^{\frac {1}{\sqrt {2}}} \, _2F_1\left (\frac {1}{\sqrt {2}},-1+\frac {1}{\sqrt {2}};1+\sqrt {2};\frac {x}{2}\right )+\left (-\frac {1}{2}\right )^{-\frac {1}{\sqrt {2}}} c_1 x^{-\frac {1}{\sqrt {2}}} \, _2F_1\left (-\frac {1}{\sqrt {2}},-1-\frac {1}{\sqrt {2}};1-\sqrt {2};\frac {x}{2}\right )\right \}\right \}\] ✓ Maple : cpu = 1.524 (sec), leaf count = 81
\[ \left \{ y \left ( x \right ) = \left ( x-2 \right ) ^{2} \left ( {\it \_C2}\,{\mbox {$_2$F$_1$}(2+{\frac {\sqrt {2}}{2}},1+{\frac {\sqrt {2}}{2}};\,1+\sqrt {2};\,{\frac {x}{2}})}{x}^{{\frac {\sqrt {2}}{2}}}+{\it \_C1}\,{\mbox {$_2$F$_1$}(2-{\frac {\sqrt {2}}{2}},1-{\frac {\sqrt {2}}{2}};\,1-\sqrt {2};\,{\frac {x}{2}})}{x}^{-{\frac {\sqrt {2}}{2}}} \right ) \right \} \]