65.8.23 problem 9 (b)

Internal problem ID [15744]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 2. The Initial Value Problem. Exercises 2.4.4, page 115
Problem number : 9 (b)
Date solved : Thursday, October 02, 2025 at 10:25:08 AM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=3 x y^{{1}/{3}} \end{align*}

With initial conditions

\begin{align*} y \left (-1\right )&=1 \\ \end{align*}

✓ Maple. Time used: 0.059 (sec). Leaf size: 9

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

\[ y = -x^{3} \]

✓ Mathematica. Time used: 0.071 (sec). Leaf size: 12

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

\begin{align*} y(x)&\to \left (x^2\right )^{3/2} \end{align*}

✗ Sympy

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

NotImplementedError : Initial conditions produced too many solutions for constants