80.3.1 problem 1

Internal problem ID [21165]
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 : 1
Date solved : Thursday, October 02, 2025 at 07:15:13 PM
CAS classification : [_quadrature]

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

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

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

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

✓ Mathematica. Time used: 0.132 (sec). Leaf size: 24

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

\begin{align*} x(t)&\to \tan (t+c_1)\\ x(t)&\to -i\\ x(t)&\to i \end{align*}

✓ Sympy. Time used: 0.162 (sec). Leaf size: 8

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

\[ x{\left (t \right )} = - \tan {\left (C_{1} - t \right )} \]