\[ (a x+b) y'(x)+c y(x)+(x-1) x y''(x)=0 \] ✓ Mathematica : cpu = 0.108355 (sec), leaf count = 146
\[\left \{\left \{y(x)\to (-1)^{b+1} c_2 x^{b+1} \, _2F_1\left (\frac {a}{2}+b-\frac {1}{2} \sqrt {a^2-2 a-4 c+1}+\frac {1}{2},\frac {a}{2}+b+\frac {1}{2} \sqrt {a^2-2 a-4 c+1}+\frac {1}{2};b+2;x\right )+c_1 \, _2F_1\left (\frac {a}{2}-\frac {1}{2} \sqrt {a^2-2 a-4 c+1}-\frac {1}{2},\frac {a}{2}+\frac {1}{2} \sqrt {a^2-2 a-4 c+1}-\frac {1}{2};-b;x\right )\right \}\right \}\] ✓ Maple : cpu = 0.039 (sec), leaf count = 110
\[y \relax (x ) = c_{1} \hypergeom \left (\left [-\frac {1}{2}+\frac {\sqrt {a^{2}-2 a -4 c +1}}{2}+\frac {a}{2}, -\frac {1}{2}-\frac {\sqrt {a^{2}-2 a -4 c +1}}{2}+\frac {a}{2}\right ], \left [-b \right ], x\right )+c_{2} x^{b +1} \hypergeom \left (\left [\frac {1}{2}-\frac {\sqrt {a^{2}-2 a -4 c +1}}{2}+\frac {a}{2}+b , \frac {1}{2}+\frac {\sqrt {a^{2}-2 a -4 c +1}}{2}+\frac {a}{2}+b \right ], \left [b +2\right ], x\right )\]