Internal problem ID [12904]
Book: DIFFERENTIAL EQUATIONS by Paul Blanchard, Robert L. Devaney, Glen R. Hall. 4th
edition. Brooks/Cole. Boston, USA. 2012
Section: Chapter 1. First-Order Differential Equations. Exercises section 1.3 page 47
Problem number: 5.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
\[ \boxed {y^{\prime }-2 y \left (-y+1\right )=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 14
dsolve(diff(y(t),t)=2*y(t)*(1-y(t)),y(t), singsol=all)
\[ y \left (t \right ) = \frac {1}{{\mathrm e}^{-2 t} c_{1} +1} \]
✓ Solution by Mathematica
Time used: 0.404 (sec). Leaf size: 33
DSolve[y'[t]==2*y[t]*(1-y[t]),y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \frac {e^{2 t}}{e^{2 t}+e^{c_1}} \\ y(t)\to 0 \\ y(t)\to 1 \\ \end{align*}