\[ a y(x)+12 x^2 y''(x)+x^4 y^{(4)}(x)+8 x^3 y^{(3)}(x)=0 \] ✓ Mathematica : cpu = 0.0087545 (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 = 0.064 (sec), leaf count = 89
\[ \left \{ y \left ( x \right ) ={\it \_C1}\,{x}^{-{\frac {1}{2}}-{\frac {1}{2}\sqrt {5-4\,\sqrt {1-a}}}}+{\it \_C2}\,{x}^{-{\frac {1}{2}}+{\frac {1}{2}\sqrt {5-4\,\sqrt {1-a}}}}+{\it \_C3}\,{x}^{-{\frac {1}{2}}-{\frac {1}{2}\sqrt {5+4\,\sqrt {1-a}}}}+{\it \_C4}\,{x}^{-{\frac {1}{2}}+{\frac {1}{2}\sqrt {5+4\,\sqrt {1-a}}}} \right \} \]