70.5.6 problem 6

Internal problem ID [18713]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 2. First order differential equations. Section 2.7 (Substitution Methods). Problems at page 108
Problem number : 6
Date solved : Thursday, October 02, 2025 at 03:22:42 PM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class B`]]

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

✓ Maple. Time used: 0.009 (sec). Leaf size: 21

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

\[ y = -\frac {x \left (1+\operatorname {LambertW}\left (-\frac {{\mathrm e}^{-4 c_1 -1}}{x^{4}}\right )\right )}{2} \]

✓ Mathematica. Time used: 3.555 (sec). Leaf size: 33

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

\begin{align*} y(x)&\to -\frac {1}{2} x \left (1+W\left (-\frac {e^{-4 c_1}}{x^4}\right )\right )\\ y(x)&\to -\frac {x}{2} \end{align*}

✗ Sympy

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

RecursionError : maximum recursion depth exceeded