44.2.1 problem 1

Internal problem ID [6933]
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 : 1
Date solved : Monday, January 27, 2025 at 02:37:15 PM
CAS classification : [_quadrature]

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

With initial conditions

\begin{align*} y \left (0\right )&=-{\frac {1}{3}} \end{align*}

✓ Solution by Maple

Time used: 0.016 (sec). Leaf size: 16

dsolve([diff(y(x),x)=y(x)-y(x)^2,y(0) = -1/3],y(x), singsol=all)
 

\[ y = -\frac {1}{4 \,{\mathrm e}^{-x}-1} \]

✓ Solution by Mathematica

Time used: 0.010 (sec). Leaf size: 16

DSolve[{D[y[x],x]==y[x]-y[x]^2,{y[0]==-1/3}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {e^x}{e^x-4} \]