Internal problem ID [15493]
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: 751.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }+\frac {3 y^{\prime }}{x}+4 y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 23
dsolve(diff(y(x),x$2)+3/x*diff(y(x),x)+4*y(x)=0,y(x), singsol=all)
\[ y = \frac {c_{1} \operatorname {BesselJ}\left (1, 2 x \right )+c_{2} \operatorname {BesselY}\left (1, 2 x \right )}{x} \]
✓ Solution by Mathematica
Time used: 0.017 (sec). Leaf size: 26
DSolve[y''[x]+3/x*y'[x]+4*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {c_1 \operatorname {BesselJ}(1,2 x)+c_2 \operatorname {BesselY}(1,2 x)}{x} \]