Internal problem ID [11693]
Book: AN INTRODUCTION TO ORDINARY DIFFERENTIAL EQUATIONS by JAMES C.
ROBINSON. Cambridge University Press 2004
Section: Chapter 10, Two tricks for nonlinear equations. Exercises page 97
Problem number: 10.5.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
\[ \boxed {x^{\prime }-k x+x^{2}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 18
dsolve(diff(x(t),t)=k*x(t)-x(t)^2,x(t), singsol=all)
\[ x \left (t \right ) = \frac {k}{1+{\mathrm e}^{-k t} c_{1} k} \]
✓ Solution by Mathematica
Time used: 0.963 (sec). Leaf size: 37
DSolve[x'[t]==k*x[t]-x[t]^2,x[t],t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \frac {k e^{k (t+c_1)}}{-1+e^{k (t+c_1)}} x(t)\to 0 x(t)\to k \end{align*}