81.5.2 problem 6-2

Internal problem ID [21540]
Book : The Differential Equations Problem Solver. VOL. I. M. Fogiel director. REA, NY. 1978. ISBN 78-63609
Section : Chapter 6. Method of grouping. Page 96.
Problem number : 6-2
Date solved : Thursday, October 02, 2025 at 07:47:15 PM
CAS classification : [[_homogeneous, `class G`], _rational]

\begin{align*} y+\left (x +x^{3} y^{2}\right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.010 (sec). Leaf size: 16

ode:=y(x)+(x+x^3*y(x)^2)*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {1}{\sqrt {\operatorname {LambertW}\left (\frac {c_1}{x^{2}}\right )}\, x} \]

✓ Mathematica. Time used: 5.542 (sec). Leaf size: 53

ode=y[x]+(x+x^3*y[x]^2)*D[y[x],x] ==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -\frac {1}{x \sqrt {W\left (\frac {e^{-2 c_1}}{x^2}\right )}}\\ y(x)&\to \frac {1}{x \sqrt {W\left (\frac {e^{-2 c_1}}{x^2}\right )}}\\ y(x)&\to 0 \end{align*}

✓ Sympy. Time used: 0.574 (sec). Leaf size: 19

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

\[ y{\left (x \right )} = e^{C_{1} + \frac {W\left (\frac {e^{- 2 C_{1}}}{x^{2}}\right )}{2}} \]