81.5.7 problem 6-7

Internal problem ID [21545]
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 : 6-7
Date solved : Thursday, October 02, 2025 at 07:47:34 PM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class B`]]

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

✓ Maple. Time used: 0.009 (sec). Leaf size: 15

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

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

✓ Mathematica. Time used: 0.965 (sec). Leaf size: 21

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

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

✓ Sympy. Time used: 0.270 (sec). Leaf size: 8

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

\[ y{\left (x \right )} = x W\left (\frac {C_{1}}{x}\right ) \]