80.5.19 problem B 19

Internal problem ID [21240]
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 5. Second order equations. Excercise 5.9 at page 119
Problem number : B 19
Date solved : Thursday, October 02, 2025 at 07:27:13 PM
CAS classification : [[_2nd_order, _missing_x]]

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

With initial conditions

\begin{align*} x \left (a \right )&=0 \\ x \left (b \right )&=0 \\ \end{align*}

✓ Maple. Time used: 0.017 (sec). Leaf size: 5

ode:=diff(diff(x(t),t),t)+x(t) = 0; 
ic:=[x(a) = 0, x(b) = 0]; 
dsolve([ode,op(ic)],x(t), singsol=all);
 

\[ x = 0 \]

✓ Mathematica. Time used: 0.044 (sec). Leaf size: 48

ode=D[x[t],{t,2}]+x[t]==0; 
ic={x[a]==0,x[b]==0}; 
DSolve[{ode,ic},x[t],t,IncludeSingularSolutions->True]
 

\begin{align*} x(t)&\to \begin {array}{cc} \{ & \begin {array}{cc} c_1 (\sin (t)-\cos (t) \tan (a)) & (\cos (a)=\cot (b) \sin (a)\lor \sin (b)=0)\land (\cos (b)=0\lor \sin (a)=0\lor \sin (b)\neq 0) \\ 0 & \text {True} \\ \end {array} \\ \end {array} \end{align*}

✓ Sympy. Time used: 0.038 (sec). Leaf size: 3

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

\[ x{\left (t \right )} = 0 \]