38.2.17 problem 17

Internal problem ID [8235]
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 : Tuesday, September 30, 2025 at 05:19:27 PM
CAS classification : [_quadrature]

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

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

ode:=diff(y(x),x) = y(x)^(2/3); 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.069 (sec). Leaf size: 20

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

\begin{align*} y(x)&\to \frac {1}{27} (x+c_1){}^3\\ y(x)&\to 0 \end{align*}

✓ Sympy. Time used: 0.102 (sec). Leaf size: 26

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-y(x)**(2/3) + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {C_{1}^{3}}{27} + \frac {C_{1}^{2} x}{9} + \frac {C_{1} x^{2}}{9} + \frac {x^{3}}{27} \]