\[ (a x+b) y'(x)+c y(x)+x (x+1) y''(x)=0 \] ✓ Mathematica : cpu = 0.105979 (sec), leaf count = 151
\[\left \{\left \{y(x)\to c_2 x^{1-b} \, _2F_1\left (\frac {a}{2}-b-\frac {1}{2} \sqrt {a^2-2 a-4 c+1}+\frac {1}{2},\frac {a}{2}-b+\frac {1}{2} \sqrt {a^2-2 a-4 c+1}+\frac {1}{2};2-b;-x\right )+c_1 \, _2F_1\left (\frac {a}{2}-\frac {1}{2} \sqrt {a^2-2 a-4 c+1}-\frac {1}{2},\frac {a}{2}+\frac {1}{2} \sqrt {a^2-2 a-4 c+1}-\frac {1}{2};b;-x\right )\right \}\right \}\] ✓ Maple : cpu = 0.048 (sec), leaf count = 124
\[y \relax (x ) = c_{1} \hypergeom \left (\left [-\frac {1}{2}+\frac {\sqrt {a^{2}-2 a -4 c +1}}{2}+\frac {a}{2}, -\frac {1}{2}-\frac {\sqrt {a^{2}-2 a -4 c +1}}{2}+\frac {a}{2}\right ], \left [a -b \right ], 1+x \right )+c_{2} \left (1+x \right )^{-a +b +1} \hypergeom \left (\left [\frac {1}{2}-\frac {\sqrt {a^{2}-2 a -4 c +1}}{2}-\frac {a}{2}+b , \frac {1}{2}+\frac {\sqrt {a^{2}-2 a -4 c +1}}{2}-\frac {a}{2}+b \right ], \left [2-a +b \right ], 1+x \right )\]