38.1.40 problem 42

Internal problem ID [8201]
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. Exercises 1.1 at page 12
Problem number : 42
Date solved : Tuesday, September 30, 2025 at 05:18:43 PM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=y^{2}+2 y-3 \end{align*}

✓ Maple. Time used: 0.010 (sec). Leaf size: 24

ode:=diff(y(x),x) = y(x)^2+2*y(x)-3; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {-3 \,{\mathrm e}^{4 x} c_1 -1}{-1+{\mathrm e}^{4 x} c_1} \]

✓ Mathematica. Time used: 0.126 (sec). Leaf size: 42

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

\begin{align*} y(x)&\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {1}{(K[1]-1) (K[1]+3)}dK[1]\&\right ][x+c_1]\\ y(x)&\to -3\\ y(x)&\to 1 \end{align*}

✓ Sympy. Time used: 0.222 (sec). Leaf size: 22

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

\[ y{\left (x \right )} = \frac {e^{4 C_{1} - 4 x} + 3}{e^{4 C_{1} - 4 x} - 1} \]