Internal problem ID [10340]
Book: A First Course in Differential Equations by J. David Logan. Third Edition. Springer-Verlag, NY.
2015.
Section: Chapter 1, First order differential equations. Section 1.1.3 Geometric. Exercises page
15
Problem number: 1.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
\[ \boxed {x^{\prime }-x \left (1-\frac {x}{4}\right )=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 17
dsolve(diff(x(t),t)=x(t)*(1-x(t)/4),x(t), singsol=all)
\[ x \left (t \right ) = \frac {4}{1+4 \,{\mathrm e}^{-t} c_{1}} \]
✓ Solution by Mathematica
Time used: 0.292 (sec). Leaf size: 32
DSolve[x'[t]==x[t]*(1-x[t]/4),x[t],t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \frac {4 e^t}{e^t+e^{4 c_1}} \\ x(t)\to 0 \\ x(t)\to 4 \\ \end{align*}