44.1.40 problem 42

Internal problem ID [6915]
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 : Monday, January 27, 2025 at 02:34:53 PM
CAS classification : [_quadrature]

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

✓ Solution by Maple

Time used: 0.013 (sec). Leaf size: 24

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

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

✓ Solution by Mathematica

Time used: 0.689 (sec). Leaf size: 40

DSolve[D[y[x],x]==y[x]^2+2*y[x]-3,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {-1-3 e^{4 (x+c_1)}}{-1+e^{4 (x+c_1)}} \\ y(x)\to -3 \\ y(x)\to 1 \\ \end{align*}