38.2.15 problem 15

Internal problem ID [8233]
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 : Tuesday, September 30, 2025 at 05:19:23 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*}

✓ Maple. Time used: 0.014 (sec). Leaf size: 5

ode:=diff(y(x),x) = 3*y(x)^(2/3); 
ic:=[y(0) = 0]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = 0 \]

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 8

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

\begin{align*} y(x)&\to x^3 \end{align*}

✓ Sympy. Time used: 0.107 (sec). Leaf size: 5

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

\[ y{\left (x \right )} = x^{3} \]