14.29.13 problem 13

Internal problem ID [2811]
Book : Differential equations and their applications, 4th ed., M. Braun
Section : Chapter 4. Qualitative theory of differential equations. Section 4.2 (Stability of linear systems). Page 383
Problem number : 13
Date solved : Tuesday, March 04, 2025 at 02:43:02 PM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 11

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

\[ x \left (t \right ) = \frac {1}{-t +c_1} \]

✓ Mathematica. Time used: 0.115 (sec). Leaf size: 18

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

\begin{align*} x(t)\to -\frac {1}{t+c_1} \\ x(t)\to 0 \\ \end{align*}

✓ Sympy. Time used: 0.139 (sec). Leaf size: 8

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

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