80.3.16 problem 17

Internal problem ID [21180]
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 3. First order nonlinear differential equations. Excercise 3.7 at page 67
Problem number : 17
Date solved : Thursday, October 02, 2025 at 07:15:54 PM
CAS classification : [_quadrature]

\begin{align*} x^{\prime }&=\sqrt {1-x^{2}} \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 8

ode:=diff(x(t),t) = (1-x(t)^2)^(1/2); 
dsolve(ode,x(t), singsol=all);
 

\[ x = \sin \left (t +c_1 \right ) \]

✓ Mathematica. Time used: 0.128 (sec). Leaf size: 28

ode=D[x[t],t]==Sqrt[1-x[t]^2]; 
ic={}; 
DSolve[{ode,ic},x[t],t,IncludeSingularSolutions->True]
 

\begin{align*} x(t)&\to \sin (t+c_1)\\ x(t)&\to -1\\ x(t)&\to 1\\ x(t)&\to \text {Interval}[\{-1,1\}] \end{align*}

✓ Sympy. Time used: 0.132 (sec). Leaf size: 7

from sympy import * 
t = symbols("t") 
x = Function("x") 
ode = Eq(-sqrt(1 - x(t)**2) + Derivative(x(t), t),0) 
ics = {} 
dsolve(ode,func=x(t),ics=ics)
 

\[ x{\left (t \right )} = \sin {\left (C_{1} + t \right )} \]