85.36.10 problem 4 (b)

Internal problem ID [22738]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter 4. Linear differential equations. A Exercises at page 171
Problem number : 4 (b)
Date solved : Thursday, October 02, 2025 at 09:14:13 PM
CAS classification : [_Lienard]

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

✓ Maple. Time used: 0.002 (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: 0.011 (sec). Leaf size: 18

ode=x*D[y[x],{x,2}]+D[y[x],{x,1}]+x*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to c_1 \operatorname {BesselJ}(0,x)+c_2 \operatorname {BesselY}(0,x) \end{align*}

✓ Sympy. Time used: 0.121 (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)
 

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