\[ \boxed { {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) =2\,{\frac {{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) }{x \left ( x-2 \right ) }}-{\frac {y \left ( x \right ) }{{x}^{2} \left ( x-2 \right ) }}=0} \]
Mathematica: cpu = 0.167521 (sec), leaf count = 104 \[ \left \{\left \{y(x)\to \left (-\frac {1}{2}\right )^{-\frac {1}{\sqrt {2}}} c_1 x^{-\frac {1}{\sqrt {2}}} \, _2F_1\left (-\frac {1}{\sqrt {2}},-1-\frac {1}{\sqrt {2}};1-\sqrt {2};\frac {x}{2}\right )+\left (-\frac {1}{2}\right )^{\frac {1}{\sqrt {2}}} c_2 x^{\frac {1}{\sqrt {2}}} \, _2F_1\left (\frac {1}{\sqrt {2}},-1+\frac {1}{\sqrt {2}};1+\sqrt {2};\frac {x}{2}\right )\right \}\right \} \]
Maple: cpu = 0.094 (sec), leaf count = 85 \[ \left \{ y \left ( x \right ) ={\it \_C1}\, {\mbox {$_2$F$_1$}(2-{\frac {\sqrt {2}}{2}},1-{\frac {\sqrt {2}}{2}};\,1-\sqrt {2};\,{\frac {x}{2}})} {x}^{-{\frac {\sqrt {2}}{2}}} \left ( x-2 \right ) ^{2}+{\it \_C2}\, {\mbox {$_2$F$_1$}(2+{\frac {\sqrt {2}}{2}},1+{\frac {\sqrt {2}}{2}};\,1+\sqrt {2};\,{\frac {x}{2}})} {x}^{{\frac {\sqrt {2}}{2}}} \left ( x-2 \right ) ^{2} \right \} \]