8.3.7 problem 7

Internal problem ID [683]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 1.4. Separable equations. Page 43
Problem number : 7
Date solved : Saturday, March 29, 2025 at 10:13:07 PM
CAS classification : [[_homogeneous, `class G`]]

\begin{align*} y^{\prime }&=4 \left (x y\right )^{{1}/{3}} \end{align*}

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

ode:=diff(y(x),x) = 4*(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: 4.806 (sec). Leaf size: 35

ode=D[y[x],x] == 4*(x*y[x])^(1/3); 
ic={}; 
DSolve[{ode,ic},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