75.24.10 problem 750

Internal problem ID [17222]
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 ODEs). Section 18.2. Expanding a solution in generalized power series. Bessels equation. Exercises page 177
Problem number : 750
Date solved : Tuesday, January 28, 2025 at 09:57:56 AM
CAS classification : [_Lienard]

\begin{align*} y^{\prime \prime }+\frac {5 y^{\prime }}{x}+y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 35

dsolve(diff(y(x),x$2)+5/x*diff(y(x),x)+y(x)=0,y(x), singsol=all)
 

\[ y = \frac {-\operatorname {BesselJ}\left (0, x\right ) c_{1} x -\operatorname {BesselY}\left (0, x\right ) c_{2} x +2 \operatorname {BesselJ}\left (1, x\right ) c_{1} +2 \operatorname {BesselY}\left (1, x\right ) c_{2}}{x^{3}} \]

✓ Solution by Mathematica

Time used: 0.017 (sec). Leaf size: 22

DSolve[D[y[x],{x,2}]+5/x*D[y[x],x]+y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {c_1 \operatorname {BesselJ}(2,x)+c_2 \operatorname {BesselY}(2,x)}{x^2} \]