\[ ((a+1) x+b) y'(x)+(x-1) x y''(x)=0 \] ✓ Mathematica : cpu = 0.0288396 (sec), leaf count = 33
\[\left \{\left \{y(x)\to \frac {c_1 x^{b+1} \, _2F_1(b+1,a+b+1;b+2;x)}{b+1}+c_2\right \}\right \}\] ✓ Maple : cpu = 0.169 (sec), leaf count = 27
\[ \left \{ y \left ( x \right ) ={\it \_C1}+{\mbox {$_2$F$_1$}(b+1,a+b+1;\,b+2;\,x)}{x}^{b+1}{\it \_C2} \right \} \]