\[ a y'(x)+(x-1) x y''(x)-2 y(x)=0 \] ✓ Mathematica : cpu = 0.21847 (sec), leaf count = 118
\[\left \{\left \{y(x)\to \frac {c_1 \left (a^2+2 a x-a+2 x^2-2 x\right )}{a^2+3 a+4}+\frac {c_2 x^{a+1} \left (a^2+2 a x-a+2 x^2-2 x\right ) (1-x)^{1-a}}{(a-1) a (a+1) \left (a^2+3 a+4\right ) \left (a^2+a (2 x-1)+2 (x-1) x\right )}\right \}\right \}\] ✓ Maple : cpu = 0.052 (sec), leaf count = 42
\[ \left \{ y \left ( x \right ) ={\it \_C1}\, \left ( {a}^{2}+a \left ( 2\,x-1 \right ) +2\,{x}^{2}-2\,x \right ) +{\frac {{\it \_C2}\,{x}^{a}x \left ( x-1 \right ) }{ \left ( x-1 \right ) ^{a}}} \right \} \]