\[ a y(x)+x^2 y''(x)=0 \] ✓ Mathematica : cpu = 0.0114753 (sec), leaf count = 42
\[\left \{\left \{y(x)\to x^{\frac {1}{2}-\frac {1}{2} \sqrt {1-4 a}} \left (c_2 x^{\sqrt {1-4 a}}+c_1\right )\right \}\right \}\]
✓ Maple : cpu = 0.012 (sec), leaf count = 35
\[ \left \{ y \left ( x \right ) ={\it \_C1}\,{x}^{{\frac {1}{2}}+{\frac {1}{2}\sqrt {1-4\,a}}}+{\it \_C2}\,{x}^{{\frac {1}{2}}-{\frac {1}{2}\sqrt {1-4\,a}}} \right \} \]