\[ \left (x-v^2\right ) y(x)+4 x^2 y''(x)+4 x y'(x)=0 \] ✓ Mathematica : cpu = 0.0315361 (sec), leaf count = 38
DSolve[(-v^2 + x)*y[x] + 4*x*Derivative[1][y][x] + 4*x^2*Derivative[2][y][x] == 0,y[x],x]
\[\left \{\left \{y(x)\to c_1 \Gamma (1-v) J_{-v}\left (\sqrt {x}\right )+c_2 \Gamma (v+1) J_v\left (\sqrt {x}\right )\right \}\right \}\] ✓ Maple : cpu = 0.01 (sec), leaf count = 19
dsolve(4*x^2*diff(diff(y(x),x),x)+4*x*diff(y(x),x)+(-v^2+x)*y(x)=0,y(x))
\[y \left (x \right ) = c_{1} \BesselJ \left (v , \sqrt {x}\right )+c_{2} \BesselY \left (v , \sqrt {x}\right )\]