44.2.17 problem 17

Internal problem ID [6949]
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. Section 1.2 Initial value problems. Exercises 1.2 at page 19
Problem number : 17
Date solved : Monday, January 27, 2025 at 02:38:02 PM
CAS classification : [_quadrature]

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

Solution by Maple

Time used: 0.001 (sec). Leaf size: 14

dsolve(diff(y(x),x)=y(x)^(2/3),y(x), singsol=all)
 
\[ y^{{1}/{3}}-\frac {x}{3}-c_{1} = 0 \]

Solution by Mathematica

Time used: 0.113 (sec). Leaf size: 20

DSolve[D[y[x],x]==y[x]^(2/3),y[x],x,IncludeSingularSolutions -> True]
 
\begin{align*} y(x)\to \frac {1}{27} (x+c_1){}^3 \\ y(x)\to 0 \\ \end{align*}