80.9.12 problem 20

Internal problem ID [21394]
Book : A Textbook on Ordinary Differential Equations by Shair Ahmad and Antonio Ambrosetti. Second edition. ISBN 978-3-319-16407-6. Springer 2015
Section : Chapter 9. Solutions by infinite series and Bessel functions. Excercise 10.6 at page 223
Problem number : 20
Date solved : Thursday, October 02, 2025 at 07:30:45 PM
CAS classification : [[_Emden, _Fowler]]

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

With initial conditions

\begin{align*} y \left (0\right )&=0 \\ y \left (1\right )&=0 \\ \end{align*}

✓ Maple. Time used: 0.045 (sec). Leaf size: 5

ode:=s*diff(diff(y(s),s),s)+lambda*y(s) = 0; 
ic:=[y(0) = 0, y(1) = 0]; 
dsolve([ode,op(ic)],y(s), singsol=all);
 

\[ y = 0 \]

✓ Mathematica. Time used: 0.243 (sec). Leaf size: 6

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

\begin{align*} y(s)&\to 0 \end{align*}

✗ Sympy

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

Timed Out