71.2.6 problem 6

Internal problem ID [14259]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 1. Introduction. Exercises 1.3, page 27
Problem number : 6
Date solved : Wednesday, March 05, 2025 at 10:41:42 PM
CAS classification : [_quadrature]

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

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

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

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

✓ Mathematica. Time used: 0.106 (sec). Leaf size: 22

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

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

✓ Sympy. Time used: 0.168 (sec). Leaf size: 22

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

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