44.5.62 problem 52

Internal problem ID [7124]
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 2.2 Separable equations. Exercises 2.2 at page 53
Problem number : 52
Date solved : Tuesday, February 04, 2025 at 12:22:56 AM
CAS classification : [_quadrature]

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 16

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

\[ -1-{\mathrm e}^{-\frac {x}{3}} c_1 +y^{{1}/{3}} = 0 \]

✓ Solution by Mathematica

Time used: 0.190 (sec). Leaf size: 39

DSolve[D[y[x],x]==y[x]^(2/3)-y[x],y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to e^{-x} \left (e^{x/3}+e^{\frac {c_1}{3}}\right ){}^3 \\ y(x)\to 0 \\ y(x)\to 1 \\ \end{align*}