38.2.1 problem 1

Internal problem ID [8219]
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 : Tuesday, September 30, 2025 at 05:19:00 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*}

✓ Maple. Time used: 0.038 (sec). Leaf size: 16

ode:=diff(y(x),x) = y(x)-y(x)^2; 
ic:=[y(0) = -1/3]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

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

✗ Mathematica

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

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✓ Sympy. Time used: 0.213 (sec). Leaf size: 10

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(y(x)**2 - y(x) + Derivative(y(x), x),0) 
ics = {y(0): -1/3} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {1}{1 - 4 e^{- x}} \]