44.4.40 problem 22

Internal problem ID [7053]
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 : 22
Date solved : Monday, January 27, 2025 at 02:42:37 PM
CAS classification : [_quadrature]

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

✓ Solution by Maple

Time used: 0.091 (sec). Leaf size: 20

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

\[ y = \frac {1}{\operatorname {LambertW}\left (-\frac {{\mathrm e}^{-x -1}}{c_{1}}\right )+1} \]

✓ Solution by Mathematica

Time used: 0.002 (sec). Leaf size: 7

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

\[ y(x)\to c_1 \]