71.4.10 problem 10

Internal problem ID [14303]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 2. The Initial Value Problem. Exercises 2.2, page 53
Problem number : 10
Date solved : Wednesday, March 05, 2025 at 10:44:35 PM
CAS classification : [[_homogeneous, `class G`]]

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

✓ Maple. Time used: 0.007 (sec). Leaf size: 87

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

\[ -\frac {x \left (\left (-4 c_{1} x^{5}+32 y^{2} c_{1} x +2 x \right ) \left (x y\right )^{{2}/{3}}+\left (x^{3}+4 y \left (x y\right )^{{1}/{3}}\right ) \left (c_{1} x^{4}-8 y^{2} c_{1} +1\right )\right )}{\left (x^{4}-8 y^{2}\right ) \left (-2 \left (x y\right )^{{2}/{3}}+x^{2}\right )^{2}} = 0 \]

✓ Mathematica. Time used: 4.811 (sec). Leaf size: 35

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

\begin{align*} y(x)\to \frac {\left (3 x^{4/3}+4 c_1\right ){}^{3/2}}{6 \sqrt {6}} \\ y(x)\to 0 \\ \end{align*}

✗ Sympy

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

Timed Out