\[ y''(x)=-\frac {y(x) \left (x \left (a^2-b^2\right )+c^2\right )}{4 (x-1) x^2}-\frac {((a+1) x-1) y'(x)}{(x-1) x} \] ✓ Mathematica : cpu = 0.149196 (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 = 0.505 (sec), leaf count = 89
\[ \left \{ y \left ( x \right ) = \left ( x-1 \right ) ^{1-a} \left ( {x}^{-{\frac {c}{2}}}{\mbox {$_2$F$_1$}(-{\frac {a}{2}}+{\frac {b}{2}}-{\frac {c}{2}}+1,-{\frac {a}{2}}-{\frac {b}{2}}-{\frac {c}{2}}+1;\,1-c;\,x)}{\it \_C2}+{x}^{{\frac {c}{2}}}{\mbox {$_2$F$_1$}(-{\frac {a}{2}}-{\frac {b}{2}}+{\frac {c}{2}}+1,-{\frac {a}{2}}+{\frac {b}{2}}+{\frac {c}{2}}+1;\,c+1;\,x)}{\it \_C1} \right ) \right \} \]