47.2.17 problem 17

Internal problem ID [7433]
Book : Ordinary differential equations and calculus of variations. Makarets and Reshetnyak. Wold Scientific. Singapore. 1995
Section : Chapter 1. First order differential equations. Section 1.2 Homogeneous equations problems. page 12
Problem number : 17
Date solved : Sunday, March 30, 2025 at 12:03:38 PM
CAS classification : [[_homogeneous, `class A`], _rational, _dAlembert]

\begin{align*} \frac {1}{x^{2}-x y+y^{2}}&=\frac {y^{\prime }}{2 y^{2}-x y} \end{align*}

✓ Maple. Time used: 0.456 (sec). Leaf size: 40

ode:=1/(x^2-x*y(x)+y(x)^2) = 1/(2*y(x)^2-x*y(x))*diff(y(x),x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \left (\operatorname {RootOf}\left (x^{2} c_1 \,\textit {\_Z}^{8}+2 x^{2} c_1 \,\textit {\_Z}^{6}-\textit {\_Z}^{4}-2 \textit {\_Z}^{2}-1\right )^{2}+2\right ) x \]

✓ Mathematica. Time used: 60.216 (sec). Leaf size: 1805

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

\begin{align*} \text {Solution too large to show}\end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(1/(x**2 - x*y(x) + y(x)**2) - Derivative(y(x), x)/(-x*y(x) + 2*y(x)**2),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out