46.3.14 problem 16

Internal problem ID [9586]
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 : 16
Date solved : Tuesday, September 30, 2025 at 06:21:03 PM
CAS classification : [_Lienard]

\begin{align*} x y^{\prime \prime }-5 y^{\prime }+x y&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 42

ode:=x*diff(diff(y(x),x),x)-5*diff(y(x),x)+x*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = -\left (c_1 \left (x^{2}-8\right ) \operatorname {BesselJ}\left (1, x\right )+c_2 \left (x^{2}-8\right ) \operatorname {BesselY}\left (1, x\right )+4 x \left (c_1 \operatorname {BesselJ}\left (0, x\right )+c_2 \operatorname {BesselY}\left (0, x\right )\right )\right ) x \]

✓ Mathematica. Time used: 0.012 (sec). Leaf size: 22

ode=x*D[y[x],{x,2}]-5*D[y[x],x]+x*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to x^3 (c_1 \operatorname {BesselJ}(3,x)+c_2 \operatorname {BesselY}(3,x)) \end{align*}

✓ Sympy. Time used: 0.111 (sec). Leaf size: 15

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x*y(x) + x*Derivative(y(x), (x, 2)) - 5*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = x^{3} \left (C_{1} J_{3}\left (x\right ) + C_{2} Y_{3}\left (x\right )\right ) \]