\[ a y(x)+x^4 y^{(4)}(x)+8 x^3 y^{(3)}(x)+12 x^2 y''(x)=0 \] ✓ Mathematica : cpu = 0.0273794 (sec), leaf count = 116
\[\left \{\left \{y(x)\to \frac {c_1 x^{-\frac {1}{2} \sqrt {5-4 \sqrt {1-a}}}+c_2 x^{\frac {1}{2} \sqrt {5-4 \sqrt {1-a}}}+c_3 x^{-\frac {1}{2} \sqrt {4 \sqrt {1-a}+5}}+c_4 x^{\frac {1}{2} \sqrt {4 \sqrt {1-a}+5}}}{\sqrt {x}}\right \}\right \}\]
✓ Maple : cpu = 0.041 (sec), leaf count = 89
\[ \left \{ y \left ( x \right ) ={\it \_C1}\,{x}^{-{\frac {1}{2}}-{\frac {1}{2}\sqrt {5-4\,\sqrt {1-a}}}}+{\it \_C2}\,{x}^{-{\frac {1}{2}}+{\frac {1}{2}\sqrt {5-4\,\sqrt {1-a}}}}+{\it \_C3}\,{x}^{-{\frac {1}{2}}-{\frac {1}{2}\sqrt {5+4\,\sqrt {1-a}}}}+{\it \_C4}\,{x}^{-{\frac {1}{2}}+{\frac {1}{2}\sqrt {5+4\,\sqrt {1-a}}}} \right \} \]