68.2.2 problem Problem 3.7(b)

Internal problem ID [14147]
Book : Differential Equations, Linear, Nonlinear, Ordinary, Partial. A.C. King, J.Billingham, S.R.Otto. Cambridge Univ. Press 2003
Section : Chapter 3 Bessel functions. Problems page 89
Problem number : Problem 3.7(b)
Date solved : Tuesday, January 28, 2025 at 06:15:55 AM
CAS classification : [[_Emden, _Fowler]]

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 23

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

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

✓ Solution by Mathematica

Time used: 0.030 (sec). Leaf size: 31

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

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