\[ a y'(x)+(x-1) x y''(x)-2 y(x)=0 \] ✓ Mathematica : cpu = 0.273209 (sec), leaf count = 118
DSolve[-2*y[x] + a*Derivative[1][y][x] + (-1 + x)*x*Derivative[2][y][x] == 0,y[x],x]
\[\left \{\left \{y(x)\to \frac {c_1 \left (a^2+2 a x-a+2 x^2-2 x\right )}{a^2+3 a+4}+\frac {c_2 x^{a+1} \left (a^2+2 a x-a+2 x^2-2 x\right ) (1-x)^{1-a}}{(a-1) a (a+1) \left (a^2+3 a+4\right ) \left (a^2+a (2 x-1)+2 (x-1) x\right )}\right \}\right \}\] ✓ Maple : cpu = 0.018 (sec), leaf count = 42
dsolve(x*(x-1)*diff(diff(y(x),x),x)+a*diff(y(x),x)-2*y(x)=0,y(x))
\[y \left (x \right ) = c_{1} \left (a^{2}+a \left (2 x -1\right )+2 x^{2}-2 x \right )+c_{2} \left (x -1\right )^{-a} x^{a} \left (x -1\right ) x\]