80.1.3 problem 4

Internal problem ID [18533]
Book : Elementary Differential Equations. By Thornton C. Fry. D Van Nostrand. NY. First Edition (1929)
Section : Chapter 1. section 5. Problems at page 19
Problem number : 4
Date solved : Tuesday, January 28, 2025 at 11:54:25 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+\frac {y^{\prime }}{x}+k^{2} 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)+k^2*y(x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.018 (sec). Leaf size: 22

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

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