\[ (x-2) (x-1) y''(x)-(2 x-3) y'(x)+y(x)=0 \] ✓ Mathematica : cpu = 0.0322662 (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 = 0.609 (sec), leaf count = 93
\[y \relax (x ) = \left (x -2\right )^{2} \left (c_{2} \hypergeom \left (\left [\frac {5}{2}+\frac {\sqrt {5}}{2}, \frac {1}{2}+\frac {\sqrt {5}}{2}\right ], \left [\sqrt {5}+1\right ], \frac {1}{x -1}\right ) \left (x -1\right )^{-\frac {1}{2}-\frac {\sqrt {5}}{2}}+c_{1} \hypergeom \left (\left [\frac {5}{2}-\frac {\sqrt {5}}{2}, \frac {1}{2}-\frac {\sqrt {5}}{2}\right ], \left [-\sqrt {5}+1\right ], \frac {1}{x -1}\right ) \left (x -1\right )^{\frac {\sqrt {5}}{2}-\frac {1}{2}}\right )\]