\[ y''(x)=-\frac {y(x) \left (x \left (a^2-b^2\right )+c^2\right )}{4 (x-1) x^2}-\frac {((a+1) x-1) y'(x)}{(x-1) x} \] ✓ Mathematica : cpu = 0.147618 (sec), leaf count = 114
\[\left \{\left \{y(x)\to i^{-c} c_1 x^{-c/2} \, _2F_1\left (\frac {a}{2}-\frac {b}{2}-\frac {c}{2},\frac {a}{2}+\frac {b}{2}-\frac {c}{2};1-c;x\right )+i^c c_2 x^{c/2} \, _2F_1\left (\frac {a}{2}-\frac {b}{2}+\frac {c}{2},\frac {a}{2}+\frac {b}{2}+\frac {c}{2};c+1;x\right )\right \}\right \}\] ✓ Maple : cpu = 0.072 (sec), leaf count = 89
\[y \relax (x ) = \left (x -1\right )^{1-a} \left (x^{-\frac {c}{2}} \hypergeom \left (\left [-\frac {a}{2}-\frac {b}{2}-\frac {c}{2}+1, -\frac {a}{2}+\frac {b}{2}-\frac {c}{2}+1\right ], \left [-c +1\right ], x\right ) c_{2}+x^{\frac {c}{2}} \hypergeom \left (\left [-\frac {a}{2}+\frac {b}{2}+\frac {c}{2}+1, -\frac {a}{2}-\frac {b}{2}+\frac {c}{2}+1\right ], \left [c +1\right ], x\right ) c_{1}\right )\]