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 = 0.0116664 (sec), leaf count = 28
\[\left \{\left \{y(x)\to \sqrt {x} \left (c_1 J_0(a x)+c_2 Y_0(a x)\right )\right \}\right \}\]
Maple ✓
cpu = 0.032 (sec), leaf count = 23
\[ \left \{ y \left ( x \right ) =\sqrt {x} \left ( {{\sl Y}_{0}\left (ax\right )}{\it \_C2}+{{\sl J}_{0}\left (ax\right )}{\it \_C1} \right ) \right \} \] 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),'implicit')
Maple raw output
y(x) = x^(1/2)*(BesselY(0,a*x)*_C2+BesselJ(0,a*x)*_C1)