Internal problem ID [13043]
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. Review Exercises for chapter 1. page
136
Problem number: 28.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
\[ \boxed {y^{\prime }-2 y+y^{2}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 17
dsolve(diff(y(t),t)= 2*y(t)-y(t)^2,y(t), singsol=all)
\[ y \left (t \right ) = \frac {2}{1+2 \,{\mathrm e}^{-2 t} c_{1}} \]
✓ Solution by Mathematica
Time used: 0.447 (sec). Leaf size: 36
DSolve[y'[t]==2*y[t]-y[t]^2,y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \frac {2 e^{2 t}}{e^{2 t}+e^{2 c_1}} \\ y(t)\to 0 \\ y(t)\to 2 \\ \end{align*}