\[ (a x+b) y'(x)+c y(x)+\left (x^2-1\right ) y''(x)=0 \] ✓ Mathematica : cpu = 0.113164 (sec), leaf count = 193
DSolve[c*y[x] + (b + a*x)*Derivative[1][y][x] + (-1 + x^2)*Derivative[2][y][x] == 0,y[x],x]
\[\left \{\left \{y(x)\to c_2 2^{\frac {1}{2} (a+b-2)} (x-1)^{\frac {1}{2} (-a-b+2)} \, _2F_1\left (-\frac {b}{2}-\frac {1}{2} \sqrt {a^2-2 a-4 c+1}+\frac {1}{2},-\frac {b}{2}+\frac {1}{2} \sqrt {a^2-2 a-4 c+1}+\frac {1}{2};-\frac {a}{2}-\frac {b}{2}+2;\frac {1-x}{2}\right )+c_1 \, _2F_1\left (\frac {a}{2}-\frac {1}{2} \sqrt {a^2-2 a-4 c+1}-\frac {1}{2},\frac {a}{2}+\frac {1}{2} \sqrt {a^2-2 a-4 c+1}-\frac {1}{2};\frac {a}{2}+\frac {b}{2};\frac {1-x}{2}\right )\right \}\right \}\] ✓ Maple : cpu = 0.058 (sec), leaf count = 134
dsolve((x^2-1)*diff(diff(y(x),x),x)+(a*x+b)*diff(y(x),x)+c*y(x)=0,y(x))
\[y \left (x \right ) = c_{1} \hypergeom \left (\left [-\frac {1}{2}+\frac {\sqrt {a^{2}-2 a -4 c +1}}{2}+\frac {a}{2}, -\frac {1}{2}-\frac {\sqrt {a^{2}-2 a -4 c +1}}{2}+\frac {a}{2}\right ], \left [\frac {a}{2}-\frac {b}{2}\right ], \frac {1}{2}+\frac {x}{2}\right )+c_{2} \left (\frac {1}{2}+\frac {x}{2}\right )^{1-\frac {a}{2}+\frac {b}{2}} \hypergeom \left (\left [\frac {1}{2}+\frac {\sqrt {a^{2}-2 a -4 c +1}}{2}+\frac {b}{2}, \frac {1}{2}-\frac {\sqrt {a^{2}-2 a -4 c +1}}{2}+\frac {b}{2}\right ], \left [2-\frac {a}{2}+\frac {b}{2}\right ], \frac {1}{2}+\frac {x}{2}\right )\]