44.4.48 problem 36

Internal problem ID [7061]
Book : A First Course in Differential Equations with Modeling Applications by Dennis G. Zill. 12 ed. Metric version. 2024. Cengage learning.
Section : Chapter 2. First order differential equations. Section 2.1 Solution curves without a solution. Exercises 2.1 at page 44
Problem number : 36
Date solved : Monday, January 27, 2025 at 02:46:33 PM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=y^{2}-y-6 \end{align*}

✓ Solution by Maple

Time used: 0.011 (sec). Leaf size: 24

dsolve(diff(y(x),x)=y(x)^2-y(x)-6,y(x), singsol=all)
 

\[ y = \frac {-3-2 \,{\mathrm e}^{5 x} c_{1}}{{\mathrm e}^{5 x} c_{1} -1} \]

✓ Solution by Mathematica

Time used: 0.475 (sec). Leaf size: 40

DSolve[D[y[x],x]==y[x]^2-y[x]-6,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {-3-2 e^{5 (x+c_1)}}{-1+e^{5 (x+c_1)}} \\ y(x)\to -2 \\ y(x)\to 3 \\ \end{align*}