65.3.4 problem 8.1 (iv)

Internal problem ID [13722]
Book : AN INTRODUCTION TO ORDINARY DIFFERENTIAL EQUATIONS by JAMES C. ROBINSON. Cambridge University Press 2004
Section : Chapter 8, Separable equations. Exercises page 72
Problem number : 8.1 (iv)
Date solved : Tuesday, January 28, 2025 at 05:59:45 AM
CAS classification : [_quadrature]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 9

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: 0.108 (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*}