\[ \boxed { x \left ( x-1 \right ) {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) +a{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) -2\,y \left ( x \right ) =0} \]
Mathematica: cpu = 0.204526 (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 = 0.031 (sec), leaf count = 42 \[ \left \{ y \left ( x \right ) = \left ( {a}^{2}+2\,ax+2\,{x}^{2}-a-2\,x \right ) {\it \_C1}+{\frac {{\it \_C2}\,{x}^{a}x \left ( x-1 \right ) }{ \left ( x-1 \right ) ^{a}}} \right \} \]