75.24.7 problem 747

Internal problem ID [17219]
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 : 747
Date solved : Tuesday, January 28, 2025 at 09:57:52 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+\frac {y^{\prime }}{x}+4 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 19

dsolve(diff(y(x),x$2)+1/x*diff(y(x),x)+4*y(x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.016 (sec). Leaf size: 22

DSolve[D[y[x],{x,2}]+1/x*D[y[x],x]+4*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_1 \operatorname {BesselJ}(0,2 x)+c_2 \operatorname {BesselY}(0,2 x) \]