88.6.12 problem 12

Internal problem ID [23994]
Book : Elementary Differential Equations. By Lee Roy Wilcox and Herbert J. Curtis. 1961 first edition. International texbook company. Scranton, Penn. USA. CAT number 61-15976
Section : Chapter 2. Differential equations of first order. Exercise at page 38
Problem number : 12
Date solved : Thursday, October 02, 2025 at 09:50:12 PM
CAS classification : [[_homogeneous, `class A`], _rational, _dAlembert]

\begin{align*} y^{\prime }&=\frac {2 y^{3}+2 x^{2} y}{x^{3}+2 x y^{2}} \end{align*}

✓ Maple. Time used: 0.012 (sec). Leaf size: 36

ode:=diff(y(x),x) = (2*y(x)^3+2*x^2*y(x))/(2*x*y(x)^2+x^3); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {{\mathrm e}^{c_1} \sqrt {2}\, x^{2}}{2 \sqrt {\frac {{\mathrm e}^{2 c_1} x^{2}}{\operatorname {LambertW}\left (2 \,{\mathrm e}^{2 c_1} x^{2}\right )}}} \]

✓ Mathematica. Time used: 1.73 (sec). Leaf size: 61

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

\begin{align*} y(x)&\to -\frac {x \sqrt {W\left (2 e^{2 c_1} x^2\right )}}{\sqrt {2}}\\ y(x)&\to \frac {x \sqrt {W\left (2 e^{2 c_1} x^2\right )}}{\sqrt {2}}\\ y(x)&\to 0 \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(Derivative(y(x), x) - (2*x**2*y(x) + 2*y(x)**3)/(x**3 + 2*x*y(x)**2),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

RecursionError : maximum recursion depth exceeded