\[ \boxed { \left ( x-1 \right ) \left ( x-2 \right ) {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) - \left ( 2\,x-3 \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) +y \left ( x \right ) =0} \]
Mathematica: cpu = 0.042505 (sec), leaf count = 64 \[ \left \{\left \{y(x)\to c_1 \left (x^2-3 x+2\right ) P_{\frac {1}{2} \left (-1+\sqrt {5}\right )}^2(2 x-3)+c_2 \left (x^2-3 x+2\right ) Q_{\frac {1}{2} \left (-1+\sqrt {5}\right )}^2(2 x-3)\right \}\right \} \]
Maple: cpu = 0.093 (sec), leaf count = 97 \[ \left \{ y \left ( x \right ) ={\it \_C1}\, {\mbox {$_2$F$_1$}({\frac {1}{2}}-{\frac {\sqrt {5}}{2}},{\frac {5}{2}}-{\frac {\sqrt {5}}{2}};\,-\sqrt {5}+1;\, \left ( x-1 \right ) ^{-1})} \left ( x-2 \right ) ^{2} \left ( x-1 \right ) ^{{\frac {\sqrt {5}}{2}}-{ \frac {1}{2}}}+{\it \_C2}\, {\mbox {$_2$F$_1$}({\frac {1}{2}}+{\frac {\sqrt {5}}{2}},{\frac {5}{2}}+{\frac {\sqrt {5}}{2}};\,\sqrt {5}+1;\, \left ( x-1 \right ) ^{-1})} \left ( x-2 \right ) ^{2} \left ( x-1 \right ) ^{-{\frac {1}{2}}-{\frac { \sqrt {5}}{2}}} \right \} \]