\[ a y'(x)+(x-1) x y''(x)-2 y(x)=0 \] ✓ Mathematica : cpu = 0.224513 (sec), leaf count = 87
\[\left \{\left \{y(x)\to \frac {\left (a^2+a (2 x-1)+2 (x-1) x\right ) \left (\frac {c_2 x^{a+1} (1-x)^{1-a}}{(a-1) a (a+1) \left (a^2+a (2 x-1)+2 (x-1) x\right )}+c_1\right )}{a^2+3 a+4}\right \}\right \}\]
✓ Maple : cpu = 0.03 (sec), leaf count = 42
\[ \left \{ y \left ( x \right ) ={\it \_C1}\, \left ( {a}^{2}+a \left ( 2\,x-1 \right ) +2\,{x}^{2}-2\,x \right ) +{\frac {{\it \_C2}\,{x}^{a}x \left ( x-1 \right ) }{ \left ( x-1 \right ) ^{a}}} \right \} \]