80.2.9 problem 12

Internal problem ID [21152]
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 2. Theory of first order differential equations. Excercise 2.6 at page 37
Problem number : 12
Date solved : Thursday, October 02, 2025 at 07:10:30 PM
CAS classification : [_quadrature]

\begin{align*} x^{\prime }&=\sin \left (x\right ) \end{align*}

✓ Maple. Time used: 0.007 (sec). Leaf size: 46

ode:=diff(x(t),t) = sin(x(t)); 
dsolve(ode,x(t), singsol=all);
 

\[ x = \arctan \left (\frac {2 \,{\mathrm e}^{t} c_1}{{\mathrm e}^{2 t} c_1^{2}+1}, \frac {-{\mathrm e}^{2 t} c_1^{2}+1}{{\mathrm e}^{2 t} c_1^{2}+1}\right ) \]

✓ Mathematica. Time used: 0.173 (sec). Leaf size: 44

ode=D[x[t],t]==Sin[x[t]]; 
ic={}; 
DSolve[{ode,ic},x[t],t,IncludeSingularSolutions->True]
 

\begin{align*} x(t)&\to -\arccos (-\tanh (t+c_1))\\ x(t)&\to \arccos (-\tanh (t+c_1))\\ x(t)&\to 0\\ x(t)&\to -\pi \\ x(t)&\to \pi \end{align*}

✗ Sympy

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

Timed Out