72.8.15 problem 28

Internal problem ID [14779]
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
Date solved : Tuesday, January 28, 2025 at 07:15:06 AM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=2 y-y^{2} \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 17

dsolve(diff(y(t),t)= 2*y(t)-y(t)^2,y(t), singsol=all)
 

\[ y = \frac {2}{1+2 c_{1} {\mathrm e}^{-2 t}} \]

✓ Solution by Mathematica

Time used: 0.260 (sec). Leaf size: 42

DSolve[D[y[t],t]==2*y[t]-y[t]^2,y[t],t,IncludeSingularSolutions -> True]
 

\begin{align*} y(t)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {1}{(K[1]-2) K[1]}dK[1]\&\right ][-t+c_1] \\ y(t)\to 0 \\ y(t)\to 2 \\ \end{align*}