\[ \left (-a x^2-1\right ) y(x)+4 x^2 y''(x)+4 x y'(x)=0 \] ✓ Mathematica : cpu = 0.0205306 (sec), leaf count = 51
DSolve[(-1 - a*x^2)*y[x] + 4*x*Derivative[1][y][x] + 4*x^2*Derivative[2][y][x] == 0,y[x],x]
\[\left \{\left \{y(x)\to \frac {c_1 e^{-\frac {\sqrt {a} x}{2}}}{\sqrt {x}}+\frac {c_2 e^{\frac {\sqrt {a} x}{2}}}{\sqrt {a} \sqrt {x}}\right \}\right \}\] ✓ Maple : cpu = 0.055 (sec), leaf count = 27
dsolve(4*x^2*diff(diff(y(x),x),x)+4*x*diff(y(x),x)-(a*x^2+1)*y(x)=0,y(x))
\[y \left (x \right ) = \frac {c_{2} \cosh \left (\frac {\sqrt {a}\, x}{2}\right )+c_{1} \sinh \left (\frac {\sqrt {a}\, x}{2}\right )}{\sqrt {x}}\]