41.1.8 problem 8

Internal problem ID [8675]
Book : Ordinary differential equations and calculus of variations. Makarets and Reshetnyak. Wold Scientific. Singapore. 1995
Section : Chapter 1. First order differential equations. Section 1.1 Separable equations problems. page 7
Problem number : 8
Date solved : Tuesday, September 30, 2025 at 05:40:45 PM
CAS classification : [_quadrature]

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

With initial conditions

\begin{align*} y \left (2\right )&=0 \\ \end{align*}

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

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

\[ y = 0 \]

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 6

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

\begin{align*} y(x)&\to 0 \end{align*}

✓ Sympy. Time used: 0.111 (sec). Leaf size: 15

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

\[ y{\left (x \right )} = x^{3} - 6 x^{2} + 12 x - 8 \]