Internal problem ID [15488]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Chapter 2 (Higher order ODE’s). Section 18.2. Expanding a solution in generalized power
series. Bessels equation. Exercises page 177
Problem number: 746.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }+\frac {y^{\prime }}{x}+\frac {y}{9}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 19
dsolve(diff(y(x),x$2)+1/x*diff(y(x),x)+1/9*y(x)=0,y(x), singsol=all)
\[ y = c_{1} \operatorname {BesselJ}\left (0, \frac {x}{3}\right )+c_{2} \operatorname {BesselY}\left (0, \frac {x}{3}\right ) \]
✓ Solution by Mathematica
Time used: 0.014 (sec). Leaf size: 26
DSolve[y''[x]+1/x*y'[x]+1/9*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_1 \operatorname {BesselJ}\left (0,\frac {x}{3}\right )+c_2 \operatorname {BesselY}\left (0,\frac {x}{3}\right ) \]