\[ ((4 a+2) x-a) y'(x)+(a-1) a y(x)+x (4 x-1) y''(x)=0 \] ✓ Mathematica : cpu = 1.0577 (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 = 0.094 (sec), leaf count = 52
\[y \relax (x ) = c_{1} \hypergeom \left (\left [\frac {a}{2}, \frac {a}{2}-\frac {1}{2}\right ], \relax [a ], 4 x \right )+c_{2} x^{1-a} \hypergeom \left (\left [1-\frac {a}{2}, -\frac {a}{2}+\frac {1}{2}\right ], \left [-a +2\right ], 4 x \right )\]