\[ a y(x)+x^2 y''(x)=0 \] ✓ Mathematica : cpu = 0.0077609 (sec), leaf count = 77
DSolve[a*y[x] + x^2*Derivative[2][y][x] == 0,y[x],x]
\[\left \{\left \{y(x)\to c_1 x^{\frac {1}{2} \left (\frac {1}{\sqrt {a}}-\frac {\sqrt {1-4 a}}{\sqrt {a}}\right ) \sqrt {a}}+c_2 x^{\frac {1}{2} \left (\frac {\sqrt {1-4 a}}{\sqrt {a}}+\frac {1}{\sqrt {a}}\right ) \sqrt {a}}\right \}\right \}\] ✓ Maple : cpu = 0.011 (sec), leaf count = 35
dsolve(x^2*diff(diff(y(x),x),x)+a*y(x)=0,y(x))
\[y \left (x \right ) = c_{1} x^{\frac {1}{2}+\frac {\sqrt {1-4 a}}{2}}+c_{2} x^{\frac {1}{2}-\frac {\sqrt {1-4 a}}{2}}\]