12.4.16 problem 19

Internal problem ID [1623]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 2, First order equations. Existence and Uniqueness of Solutions of Nonlinear Equations. Section 2.3 Page 60
Problem number : 19
Date solved : Saturday, March 29, 2025 at 11:08:13 PM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=3 x \left (y-1\right )^{{1}/{3}} \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=9 \end{align*}

✓ Maple. Time used: 0.176 (sec). Leaf size: 26

ode:=diff(y(x),x) = 3*x*(y(x)-1)^(1/3); 
ic:=y(0) = 9; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ y = \sqrt {x^{2}+4}\, x^{2}+4 \sqrt {x^{2}+4}+1 \]

✓ Mathematica. Time used: 0.124 (sec). Leaf size: 16

ode=D[y[x],x]==3*x*(y[x]-1)^(1/3); 
ic=y[0]==9; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \left (x^2+4\right )^{3/2}+1 \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-3*x*(y(x) - 1)**(1/3) + Derivative(y(x), x),0) 
ics = {y(0): 9} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : Initial conditions produced too many solutions for constants