\[ \boxed { {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) =-{\frac { \left ( \left ( a+1 \right ) x-1 \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) }{x \left ( x-1 \right ) }}-1/4\,{\frac { \left ( \left ( {a}^{2}-{b}^{2} \right ) x+{c}^{2} \right ) y \left ( x \right ) }{{x}^{2} \left ( x-1 \right ) }}=0} \]
Mathematica: cpu = 0.198525 (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 = 0.062 (sec), leaf count = 97 \[ \left \{ y \left ( x \right ) ={\it \_C1}\, \left ( x-1 \right ) ^{1-a}{x} ^{{\frac {c}{2}}} {\mbox {$_2$F$_1$}(-{\frac {a}{2}}-{\frac {b}{2}}+{\frac {c}{2}}+1,-{\frac {a}{2}}+{\frac {b}{2}}+{\frac {c}{2}}+1;\,c+1;\,x)} +{\it \_C2}\, \left ( x-1 \right ) ^{1-a}{x}^{-{\frac {c}{2}}} {\mbox {$_2$F$_1$}(-{\frac {a}{2}}-{\frac {b}{2}}-{\frac {c}{2}}+1,-{\frac {a}{2}}+{\frac {b}{2}}-{\frac {c}{2}}+1;\,1-c;\,x)} \right \} \]