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 : Monday, January 27, 2025 at 06:14:10 AM
CAS classification : [_quadrature]

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

✓ Solution by Maple

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

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

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

✓ Solution by Mathematica

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

DSolve[D[x[t],t]==x[t]^2,x[t],t,IncludeSingularSolutions -> True]
 

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