71.8.22 problem 9 (a)

Internal problem ID [14385]
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 (a)
Date solved : Monday, March 31, 2025 at 12:20:47 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 {3}{2}} \end{align*}

✓ Maple. Time used: 0.358 (sec). Leaf size: 37

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

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

✓ Mathematica. Time used: 0.235 (sec). Leaf size: 36

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

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

✗ 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): 3/2} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : Initial conditions produced too many solutions for constants