Internal problem ID [11063]
Book: Differential Equations, Linear, Nonlinear, Ordinary, Partial. A.C. King, J.Billingham, S.R.Otto.
Cambridge Univ. Press 2003
Section: Chapter 3 Bessel functions. Problems page 89
Problem number: Problem 3.7(b).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler]]
\[ \boxed {x y^{\prime \prime }+y^{\prime }+y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 23
dsolve(x*diff(y(x),x$2)+diff(y(x),x)+y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = c_{1} \operatorname {BesselJ}\left (0, 2 \sqrt {x}\right )+c_{2} \operatorname {BesselY}\left (0, 2 \sqrt {x}\right ) \]
✓ Solution by Mathematica
Time used: 0.011 (sec). Leaf size: 27
DSolve[x*y''[x]+y'[x]+y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 \, _0\tilde {F}_1(;1;-x)+2 c_2 Y_0\left (2 \sqrt {x}\right ) \\ \end{align*}