\[ (a x+b) y'(x)+c y(x)+(x-1) x y''(x)=0 \] ✓ Mathematica : cpu = 0.182206 (sec), leaf count = 130
\[\left \{\left \{y(x)\to (-1)^{b+1} c_2 x^{b+1} \, _2F_1\left (\frac {1}{2} \left (a+2 b-\sqrt {a^2-2 a-4 c+1}+1\right ),\frac {1}{2} \left (a+2 b+\sqrt {a^2-2 a-4 c+1}+1\right );b+2;x\right )+c_1 \, _2F_1\left (\frac {1}{2} \left (a-\sqrt {a^2-2 a-4 c+1}-1\right ),\frac {1}{2} \left (a+\sqrt {a^2-2 a-4 c+1}-1\right );-b;x\right )\right \}\right \}\]
✓ Maple : cpu = 0.059 (sec), leaf count = 110
\[ \left \{ y \left ( x \right ) ={\it \_C1}\,{\mbox {$_2$F$_1$}(-{\frac {1}{2}}-{\frac {1}{2}\sqrt {{a}^{2}-2\,a-4\,c+1}}+{\frac {a}{2}},-{\frac {1}{2}}+{\frac {1}{2}\sqrt {{a}^{2}-2\,a-4\,c+1}}+{\frac {a}{2}};\,-b;\,x)}+{\it \_C2}\,{x}^{b+1}{\mbox {$_2$F$_1$}({\frac {1}{2}}-{\frac {1}{2}\sqrt {{a}^{2}-2\,a-4\,c+1}}+{\frac {a}{2}}+b,{\frac {1}{2}}+{\frac {1}{2}\sqrt {{a}^{2}-2\,a-4\,c+1}}+{\frac {a}{2}}+b;\,b+2;\,x)} \right \} \]