\[ ((4 a+2) x-a) y'(x)+(a-1) a y(x)+x (4 x-1) y''(x)=0 \] ✓ Mathematica : cpu = 1.19539 (sec), leaf count = 269
\[\left \{\left \{y(x)\to c_2 x^{-a/2} \left (\sqrt {4 x-1}+i\right )^{\frac {1}{2}+\frac {1}{2} i \sqrt {-(a-1)^2}} \left (-\sqrt {4 x-1}+i\right )^{\frac {1}{2}-\frac {1}{2} i \sqrt {-(a-1)^2}} \int _1^x-\frac {\left (i-\sqrt {4 K[1]-1}\right )^{i \sqrt {-(a-1)^2}} \left (\sqrt {4 K[1]-1}+i\right )^{-i \sqrt {-(a-1)^2}-1}}{\sqrt {1-4 K[1]} \left (\sqrt {4 K[1]-1}-i\right )}dK[1]+c_1 x^{-a/2} \left (\sqrt {4 x-1}+i\right )^{\frac {1}{2}+\frac {1}{2} i \sqrt {-(a-1)^2}} \left (-\sqrt {4 x-1}+i\right )^{\frac {1}{2}-\frac {1}{2} i \sqrt {-(a-1)^2}}\right \}\right \}\] ✓ Maple : cpu = 0.238 (sec), leaf count = 52
\[ \left \{ y \left ( x \right ) ={\it \_C1}\,{\mbox {$_2$F$_1$}({\frac {a}{2}},{\frac {a}{2}}-{\frac {1}{2}};\,a;\,4\,x)}+{\it \_C2}\,{x}^{1-a}{\mbox {$_2$F$_1$}(1-{\frac {a}{2}},-{\frac {a}{2}}+{\frac {1}{2}};\,-a+2;\,4\,x)} \right \} \]