7.17.2 problem 2

Internal problem ID [515]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 3. Power series methods. Section 3.6 (Applications of Bessel functions). Problems at page 261
Problem number : 2
Date solved : Monday, January 27, 2025 at 02:54:18 AM
CAS classification : [_Lienard]

\begin{align*} x y^{\prime \prime }+3 y^{\prime }+y x&=0 \end{align*}

✓ Solution by Maple

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

dsolve(x*diff(y(x),x$2)+3*diff(y(x),x)+x*y(x)=0,y(x), singsol=all)
 

\[ y = \frac {c_1 \operatorname {BesselJ}\left (1, x\right )+c_2 \operatorname {BesselY}\left (1, x\right )}{x} \]

✓ Solution by Mathematica

Time used: 0.015 (sec). Leaf size: 22

DSolve[x*D[y[x],{x,2}]+3*D[y[x],x]+x*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {c_1 \operatorname {BesselJ}(1,x)+c_2 \operatorname {BesselY}(1,x)}{x} \]