7.3.7 problem 7

Internal problem ID [47]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 1. First order differential equations. Section 1.4 (separable equations). Problems at page 43
Problem number : 7
Date solved : Saturday, March 29, 2025 at 04:27:35 PM
CAS classification : [[_homogeneous, `class G`]]

\begin{align*} y^{\prime }&=64^{{1}/{3}} \left (x y\right )^{{1}/{3}} \end{align*}

✓ Maple. Time used: 0.005 (sec). Leaf size: 91

ode:=diff(y(x),x) = 64^(1/3)*(x*y(x))^(1/3); 
dsolve(ode,y(x), singsol=all);
 

\[ -\frac {32 x \left (\left (-c_1 \,x^{5}+\frac {y^{2} c_1 x}{8}+\frac {x}{16}\right ) \left (x y\right )^{{2}/{3}}+\left (c_1 \,x^{4}-\frac {y^{2} c_1}{8}+\frac {1}{8}\right ) \left (x^{3}+\frac {y \left (x y\right )^{{1}/{3}}}{4}\right )\right )}{\left (8 x^{4}-y^{2}\right ) \left (-\left (x y\right )^{{2}/{3}}+2 x^{2}\right )^{2}} = 0 \]

✓ Mathematica. Time used: 4.79 (sec). Leaf size: 35

ode=D[y[x],x]==(64*x*y[x])^(1/3); 
DSolve[ode,y[x],x,IncludeSingularSolutions->True]
 

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

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-4*(x*y(x))**(1/3) + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out