44.2.15 problem 15

Internal problem ID [6947]
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 : 15
Date solved : Monday, January 27, 2025 at 02:37:56 PM
CAS classification : [_quadrature]

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

With initial conditions

\begin{align*} y \left (0\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 5

dsolve([diff(y(x),x)=3*y(x)^(2/3),y(0) = 0],y(x), singsol=all)
 

\[ y = 0 \]

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 8

DSolve[{D[y[x],x]==3*y[x]^(2/3),{y[0]==0}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to x^3 \]