\[ (x-2) (x-1) y''(x)-(2 x-3) y'(x)+y(x)=0 \] ✓ Mathematica : cpu = 0.0477343 (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 = 0.437 (sec), leaf count = 93
\[ \left \{ y \left ( x \right ) = \left ( x-2 \right ) ^{2} \left ( {\it \_C2}\,{\mbox {$_2$F$_1$}({\frac {1}{2}}+{\frac {\sqrt {5}}{2}},{\frac {5}{2}}+{\frac {\sqrt {5}}{2}};\,\sqrt {5}+1;\, \left ( x-1 \right ) ^{-1})} \left ( x-1 \right ) ^{-{\frac {1}{2}}-{\frac {\sqrt {5}}{2}}}+{\it \_C1}\,{\mbox {$_2$F$_1$}({\frac {5}{2}}-{\frac {\sqrt {5}}{2}},{\frac {1}{2}}-{\frac {\sqrt {5}}{2}};\,-\sqrt {5}+1;\, \left ( x-1 \right ) ^{-1})} \left ( x-1 \right ) ^{{\frac {\sqrt {5}}{2}}-{\frac {1}{2}}} \right ) \right \} \]