\[ (a x+b) y'(x)+c y(x)+(x-1) x y''(x)=0 \] ✓ Mathematica : cpu = 0.0828506 (sec), leaf count = 146
DSolve[c*y[x] + (b + a*x)*Derivative[1][y][x] + (-1 + x)*x*Derivative[2][y][x] == 0,y[x],x]
\[\left \{\left \{y(x)\to (-1)^{b+1} c_2 x^{b+1} \operatorname {Hypergeometric2F1}\left (\frac {a}{2}+b-\frac {1}{2} \sqrt {a^2-2 a-4 c+1}+\frac {1}{2},\frac {a}{2}+b+\frac {1}{2} \sqrt {a^2-2 a-4 c+1}+\frac {1}{2},b+2,x\right )+c_1 \operatorname {Hypergeometric2F1}\left (\frac {a}{2}-\frac {1}{2} \sqrt {a^2-2 a-4 c+1}-\frac {1}{2},\frac {a}{2}+\frac {1}{2} \sqrt {a^2-2 a-4 c+1}-\frac {1}{2},-b,x\right )\right \}\right \}\] ✓ Maple : cpu = 0.093 (sec), leaf count = 110
dsolve(x*(x-1)*diff(diff(y(x),x),x)+(a*x+b)*diff(y(x),x)+y(x)*c=0,y(x))
\[y \left (x \right ) = c_{1} \operatorname {hypergeom}\left (\left [-\frac {1}{2}+\frac {\sqrt {a^{2}-2 a -4 c +1}}{2}+\frac {a}{2}, -\frac {1}{2}-\frac {\sqrt {a^{2}-2 a -4 c +1}}{2}+\frac {a}{2}\right ], \left [-b \right ], x\right )+c_{2} x^{b +1} \operatorname {hypergeom}\left (\left [\frac {1}{2}-\frac {\sqrt {a^{2}-2 a -4 c +1}}{2}+\frac {a}{2}+b , \frac {1}{2}+\frac {\sqrt {a^{2}-2 a -4 c +1}}{2}+\frac {a}{2}+b \right ], \left [b +2\right ], x\right )\]