44.2.2 problem 2

Internal problem ID [6934]
Book : A First Course in Differential Equations with Modeling Applications by Dennis G. Zill. 12 ed. Metric version. 2024. Cengage learning.
Section : Chapter 1. Introduction to differential equations. Section 1.2 Initial value problems. Exercises 1.2 at page 19
Problem number : 2
Date solved : Monday, January 27, 2025 at 02:37:17 PM
CAS classification : [_quadrature]

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

With initial conditions

\begin{align*} y \left (-1\right )&=2 \end{align*}

✓ Solution by Maple

Time used: 0.020 (sec). Leaf size: 16

dsolve([diff(y(x),x)=y(x)-y(x)^2,y(-1) = 2],y(x), singsol=all)
 

\[ y = -\frac {2}{{\mathrm e}^{-x -1}-2} \]

✓ Solution by Mathematica

Time used: 0.008 (sec). Leaf size: 23

DSolve[{D[y[x],x]==y[x]-y[x]^2,{y[-1]==2}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {2 e^{x+1}}{2 e^{x+1}-1} \]