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 : Wednesday, March 05, 2025 at 02:53:00 AM
CAS classification : [_quadrature]

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

With initial conditions

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

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

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

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

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

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

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

✓ Sympy. Time used: 0.405 (sec). Leaf size: 15

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

\[ y{\left (x \right )} = \frac {1}{1 - \frac {e^{- x}}{2 e}} \]