28.1.14 problem 14

Internal problem ID [4320]
Book : Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section : Chapter 2. First-Order and Simple Higher-Order Differential Equations. Page 78
Problem number : 14
Date solved : Sunday, March 30, 2025 at 02:59:33 AM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} x^{2}-x y+y^{2}-x y y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.012 (sec). Leaf size: 19

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

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

✓ Mathematica. Time used: 3.227 (sec). Leaf size: 25

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

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

✗ Sympy

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

RecursionError : maximum recursion depth exceeded