80.3.3 problem 3

Internal problem ID [21167]
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 : 3
Date solved : Thursday, October 02, 2025 at 07:15:16 PM
CAS classification : [_quadrature]

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

With initial conditions

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

✓ Maple. Time used: 0.019 (sec). Leaf size: 16

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

\[ x = \frac {1}{-1+2 \,{\mathrm e}^{1-t}} \]

✓ Mathematica. Time used: 0.007 (sec). Leaf size: 19

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

\begin{align*} x(t)&\to -\frac {e^t}{e^t-2 e} \end{align*}

✓ Sympy. Time used: 0.185 (sec). Leaf size: 14

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

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