\[ a y(x)+x^4 y^{(4)}(x)+8 x^3 y^{(3)}(x)+12 x^2 y''(x)=0 \] ✓ Mathematica : cpu = 0.0092596 (sec), leaf count = 122
\[\left \{\left \{y(x)\to c_1 x^{\frac {1}{2} \left (-\sqrt {5-4 \sqrt {1-a}}-1\right )}+c_2 x^{\frac {1}{2} \left (\sqrt {5-4 \sqrt {1-a}}-1\right )}+c_3 x^{\frac {1}{2} \left (-\sqrt {4 \sqrt {1-a}+5}-1\right )}+c_4 x^{\frac {1}{2} \left (\sqrt {4 \sqrt {1-a}+5}-1\right )}\right \}\right \}\] ✓ Maple : cpu = 0.033 (sec), leaf count = 89
\[y \relax (x ) = c_{1} x^{-\frac {1}{2}-\frac {\sqrt {5-4 \sqrt {1-a}}}{2}}+c_{2} x^{-\frac {1}{2}+\frac {\sqrt {5-4 \sqrt {1-a}}}{2}}+c_{3} x^{-\frac {1}{2}-\frac {\sqrt {5+4 \sqrt {1-a}}}{2}}+c_{4} x^{-\frac {1}{2}+\frac {\sqrt {5+4 \sqrt {1-a}}}{2}}\]