Internal problem ID [12663]
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 1.6 page 89
Problem number: 37 (ii).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
\[ \boxed {y^{2}+y^{\prime }-y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 14
dsolve(diff(y(t),t)=y(t)-y(t)^2,y(t), singsol=all)
\[ y \left (t \right ) = \frac {1}{1+c_{1} {\mathrm e}^{-t}} \]
✓ Solution by Mathematica
Time used: 0.42 (sec). Leaf size: 29
DSolve[y'[t]==y[t]-y[t]^2,y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \frac {e^t}{e^t+e^{c_1}} y(t)\to 0 y(t)\to 1 \end{align*}