\[ (a x+b) y'(x)+c y(x)+x (x+1) y''(x)=0 \] ✓ Mathematica : cpu = 0.167176 (sec), leaf count = 131
\[\left \{\left \{y(x)\to c_2 x^{1-b} \, _2F_1\left (\frac {1}{2} \left (a-2 b-\sqrt {a^2-2 a-4 c+1}+1\right ),\frac {1}{2} \left (a-2 b+\sqrt {a^2-2 a-4 c+1}+1\right );2-b;-x\right )+c_1 \, _2F_1\left (\frac {1}{2} \left (a-\sqrt {a^2-2 a-4 c+1}-1\right ),\frac {1}{2} \left (a+\sqrt {a^2-2 a-4 c+1}-1\right );b;-x\right )\right \}\right \}\]
✓ Maple : cpu = 0.056 (sec), leaf count = 124
\[ \left \{ y \left ( x \right ) ={\it \_C1}\,{\mbox {$_2$F$_1$}(-{\frac {1}{2}}-{\frac {1}{2}\sqrt {{a}^{2}-2\,a-4\,c+1}}+{\frac {a}{2}},-{\frac {1}{2}}+{\frac {1}{2}\sqrt {{a}^{2}-2\,a-4\,c+1}}+{\frac {a}{2}};\,a-b;\,1+x)}+{\it \_C2}\, \left ( 1+x \right ) ^{-a+b+1}{\mbox {$_2$F$_1$}({\frac {1}{2}}+{\frac {1}{2}\sqrt {{a}^{2}-2\,a-4\,c+1}}-{\frac {a}{2}}+b,{\frac {1}{2}}-{\frac {1}{2}\sqrt {{a}^{2}-2\,a-4\,c+1}}-{\frac {a}{2}}+b;\,2-a+b;\,1+x)} \right \} \]