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 : Sunday, March 30, 2025 at 11:29:33 AM
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,ic],y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.01 (sec). Leaf size: 16

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

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

✓ Sympy. Time used: 0.400 (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)
 

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