Internal problem ID [11673]
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: 8.7.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
\[ \boxed {x^{\prime }-k x+x^{2}=0} \] With initial conditions \begin {align*} [x \left (0\right ) = x_{0}] \end {align*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 22
dsolve([diff(x(t),t)=k*x(t)-x(t)^2,x(0) = x__0],x(t), singsol=all)
\[ x \left (t \right ) = \frac {k x_{0}}{\left (-x_{0} +k \right ) {\mathrm e}^{-k t}+x_{0}} \]
✓ Solution by Mathematica
Time used: 1.052 (sec). Leaf size: 26
DSolve[{x'[t]==k*x[t]-x[t]^2,{x[0]==x0}},x[t],t,IncludeSingularSolutions -> True]
\[ x(t)\to \frac {k \text {x0} e^{k t}}{\text {x0} \left (e^{k t}-1\right )+k} \]