71.8.24 problem 9 (c)

Internal problem ID [14387]
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 (c)
Date solved : Monday, March 31, 2025 at 12:21:43 PM
CAS classification : [_separable]

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

With initial conditions

\begin{align*} y \left (-1\right )&={\frac {1}{2}} \end{align*}

✓ Maple. Time used: 0.271 (sec). Leaf size: 30

ode:=diff(y(x),x) = 3*x*y(x)^(1/3); 
ic:=y(-1) = 1/2; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ y = \frac {\sqrt {4 x^{2}+2 \,2^{{1}/{3}}-4}\, \left (2 x^{2}+2^{{1}/{3}}-2\right )}{4} \]

✓ Mathematica. Time used: 0.099 (sec). Leaf size: 30

ode=D[y[x],x]==3*x*y[x]^(1/3); 
ic={y[-1]==1/2}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✗ 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): 1/2} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : Initial conditions produced too many solutions for constants