\[ ((4 a+2) x-a) y'(x)+(a-1) a y(x)+x (4 x-1) y''(x)=0 \] ✓ Mathematica : cpu = 0.208498 (sec), leaf count = 195
DSolve[(-1 + a)*a*y[x] + (-a + (2 + 4*a)*x)*Derivative[1][y][x] + x*(-1 + 4*x)*Derivative[2][y][x] == 0,y[x],x]
\[\left \{\left \{y(x)\to \frac {2 c_1 \sqrt [4]{4 x-1} x^{\frac {1}{2}-\frac {a}{2}} e^{\sqrt {-(a-1)^2} \arctan \left (\sqrt {4 x-1}\right )}}{\sqrt [4]{1-4 x}}-\frac {c_2 \sqrt [4]{4 x-1} x^{\frac {1}{2}-\frac {a}{2}} \left (1-i \sqrt {4 x-1}\right )^{-i \sqrt {-(a-1)^2}} \left (1+i \sqrt {4 x-1}\right )^{i \sqrt {-(a-1)^2}} e^{\sqrt {-(a-1)^2} \arctan \left (\sqrt {4 x-1}\right )}}{2 \sqrt {-(a-1)^2} \sqrt [4]{1-4 x}}\right \}\right \}\] ✓ Maple : cpu = 0.099 (sec), leaf count = 52
dsolve(x*(4*x-1)*diff(diff(y(x),x),x)+((4*a+2)*x-a)*diff(y(x),x)+a*(a-1)*y(x)=0,y(x))
\[y \left (x \right ) = c_{1} \operatorname {hypergeom}\left (\left [\frac {a}{2}, \frac {a}{2}-\frac {1}{2}\right ], \left [a \right ], 4 x \right )+c_{2} x^{1-a} \operatorname {hypergeom}\left (\left [1-\frac {a}{2}, -\frac {a}{2}+\frac {1}{2}\right ], \left [-a +2\right ], 4 x \right )\]