52.3.12 problem 14

Internal problem ID [8298]
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 : 14
Date solved : Wednesday, March 05, 2025 at 05:34:25 AM
CAS classification : [_Lienard]

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 19

ode:=x*diff(diff(y(x),x),x)+3*diff(y(x),x)+x*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

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

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

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

✓ Sympy. Time used: 0.205 (sec). Leaf size: 14

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x*y(x) + x*Derivative(y(x), (x, 2)) + 3*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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