Internal problem ID [15492]
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: 750.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [_Lienard]
\[ \boxed {y^{\prime \prime }+\frac {5 y^{\prime }}{x}+y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 35
dsolve(diff(y(x),x$2)+5/x*diff(y(x),x)+y(x)=0,y(x), singsol=all)
\[ y = \frac {-\operatorname {BesselY}\left (0, x\right ) c_{2} x -\operatorname {BesselJ}\left (0, x\right ) c_{1} x +2 \operatorname {BesselY}\left (1, x\right ) c_{2} +2 \operatorname {BesselJ}\left (1, x\right ) c_{1}}{x^{3}} \]
✓ Solution by Mathematica
Time used: 0.015 (sec). Leaf size: 22
DSolve[y''[x]+5/x*y'[x]+y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {c_1 \operatorname {BesselJ}(2,x)+c_2 \operatorname {BesselY}(2,x)}{x^2} \]