\[ \boxed { x \left ( 4\,x-1 \right ) {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) + \left ( \left ( 4\,a+2 \right ) x-a \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) +a \left ( a-1 \right ) y \left ( x \right ) =0} \]
Mathematica: cpu = 0.335543 (sec), leaf count = 134 \[ \left \{\left \{y(x)\to \frac {2 c_1 \sqrt [4]{4 x-1} x^{\frac {1}{2}-\frac {a}{2}} e^{\sqrt {-(a-1)^2} \tan ^{-1}\left (\sqrt {4 x-1}\right )}}{\sqrt [4]{1-4 x}}-\frac {c_2 \sqrt [4]{4 x-1} x^{\frac {1}{2}-\frac {a}{2}} e^{-\sqrt {-(a-1)^2} \tan ^{-1}\left (\sqrt {4 x-1}\right )}}{2 \sqrt {-(a-1)^2} \sqrt [4]{1-4 x}}\right \}\right \} \]
Maple: cpu = 0.079 (sec), leaf count = 52 \[ \left \{ y \left ( x \right ) ={\it \_C1}\, {\mbox {$_2$F$_1$}({\frac {a}{2}},{\frac {a}{2}}-{\frac {1}{2}};\,a;\,4\,x)} +{\it \_C2}\,{x}^{1-a} {\mbox {$_2$F$_1$}(1-{\frac {a}{2}},-{\frac {a}{2}}+{\frac {1}{2}};\,-a+2;\,4\,x)} \right \} \]