52.3.5 problem 5

Internal problem ID [8291]
Book : DIFFERENTIAL EQUATIONS with Boundary Value Problems. DENNIS G. ZILL, WARREN S. WRIGHT, MICHAEL R. CULLEN. Brooks/Cole. Boston, MA. 2013. 8th edition.
Section : CHAPTER 6 SERIES SOLUTIONS OF LINEAR EQUATIONS. 6.4 SPECIAL FUNCTIONS. EXERCISES 6.4. Page 267
Problem number : 5
Date solved : Sunday, March 30, 2025 at 12:51:04 PM
CAS classification : [_Lienard]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 15

ode:=x*diff(diff(y(x),x),x)+diff(y(x),x)+x*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.014 (sec). Leaf size: 18

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

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

✓ Sympy. Time used: 0.183 (sec). Leaf size: 12

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x*y(x) + x*Derivative(y(x), (x, 2)) + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} J_{0}\left (x\right ) + C_{2} Y_{0}\left (x\right ) \]