\[ \left (4 a^2 x^2+1\right ) y(x)+4 x^2 y''(x)=0 \] ✓ Mathematica : cpu = 0.0089455 (sec), leaf count = 32
DSolve[(1 + 4*a^2*x^2)*y[x] + 4*x^2*Derivative[2][y][x] == 0,y[x],x]
\[\left \{\left \{y(x)\to c_1 \sqrt {x} J_0(a x)+c_2 \sqrt {x} Y_0(a x)\right \}\right \}\] ✓ Maple : cpu = 0.034 (sec), leaf count = 23
dsolve(4*x^2*diff(diff(y(x),x),x)+(4*a^2*x^2+1)*y(x)=0,y(x))
\[y \left (x \right ) = \sqrt {x}\, \left (\BesselY \left (0, a x \right ) c_{2}+\BesselJ \left (0, a x \right ) c_{1}\right )\]