Internal problem ID [9607]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1272.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {4 x^{2} y^{\prime \prime }+\left (4 a^{2} x^{2}+1\right ) y=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 25
dsolve(4*x^2*diff(diff(y(x),x),x)+(4*a^2*x^2+1)*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = c_{1} \sqrt {x}\, \operatorname {BesselJ}\left (0, a x \right )+c_{2} \sqrt {x}\, \operatorname {BesselY}\left (0, a x \right ) \]
✓ Solution by Mathematica
Time used: 0.023 (sec). Leaf size: 28
DSolve[(1 + 4*a^2*x^2)*y[x] + 4*x^2*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \sqrt {x} (c_1 \operatorname {BesselJ}(0,a x)+c_2 \operatorname {BesselY}(0,a x)) \]