ODE
\[ \left (4 a^2 x^2+1\right ) y(x)+4 x^2 y''(x)=0 \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.165477 (sec), leaf count = 28
\[\left \{\left \{y(x)\to \sqrt {x} (c_1 J_0(a x)+c_2 Y_0(a x))\right \}\right \}\]
Maple ✓
cpu = 0.043 (sec), leaf count = 25
\[\left [y \left (x \right ) = \textit {\_C1} \sqrt {x}\, \BesselJ \left (0, a x \right )+\textit {\_C2} \sqrt {x}\, \BesselY \left (0, a x \right )\right ]\] Mathematica raw input
DSolve[(1 + 4*a^2*x^2)*y[x] + 4*x^2*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> Sqrt[x]*(BesselJ[0, a*x]*C[1] + BesselY[0, a*x]*C[2])}}
Maple raw input
dsolve(4*x^2*diff(diff(y(x),x),x)+(4*a^2*x^2+1)*y(x) = 0, y(x))
Maple raw output
[y(x) = _C1*x^(1/2)*BesselJ(0,a*x)+_C2*x^(1/2)*BesselY(0,a*x)]