71.8.26 problem 9 (e)

Internal problem ID [14389]
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 (e)
Date solved : Monday, March 31, 2025 at 12:22:08 PM
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: 0.153 (sec). Leaf size: 7

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

\[ y = x^{3} \]

✓ Mathematica. Time used: 0.105 (sec). Leaf size: 67

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 \frac {\left (2 x^2-i \sqrt {3}-3\right )^{3/2}}{2 \sqrt {2}} \\ y(x)\to \frac {\left (2 x^2+i \sqrt {3}-3\right )^{3/2}}{2 \sqrt {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