\[ y''(x)=-\frac {y(x) \left (x \left (a^2-b^2\right )+c^2\right )}{4 (x-1) x^2}-\frac {((a+1) x-1) y'(x)}{(x-1) x} \] ✓ Mathematica : cpu = 0.204612 (sec), leaf count = 89
\[\left \{\left \{y(x)\to i^{-c} x^{-c/2} \left (c_1 \, _2F_1\left (\frac {1}{2} (a-b-c),\frac {1}{2} (a+b-c);1-c;x\right )+i^{2 c} c_2 x^c \, _2F_1\left (\frac {1}{2} (a-b+c),\frac {1}{2} (a+b+c);c+1;x\right )\right )\right \}\right \}\]
✓ Maple : cpu = 0.1 (sec), leaf count = 89
\[ \left \{ y \left ( x \right ) = \left ( x-1 \right ) ^{1-a} \left ( {x}^{-{\frac {c}{2}}}{\mbox {$_2$F$_1$}(-{\frac {a}{2}}-{\frac {b}{2}}-{\frac {c}{2}}+1,-{\frac {a}{2}}+{\frac {b}{2}}-{\frac {c}{2}}+1;\,1-c;\,x)}{\it \_C2}+{x}^{{\frac {c}{2}}}{\mbox {$_2$F$_1$}(-{\frac {a}{2}}-{\frac {b}{2}}+{\frac {c}{2}}+1,-{\frac {a}{2}}+{\frac {b}{2}}+{\frac {c}{2}}+1;\,c+1;\,x)}{\it \_C1} \right ) \right \} \]