75.12.12 problem 286

Internal problem ID [16807]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Section 12. Miscellaneous problems. Exercises page 93
Problem number : 286
Date solved : Monday, March 31, 2025 at 03:22:00 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: 0.451 (sec). Leaf size: 40

ode:=1/(y(x)^2-x*y(x)+x^2) = diff(y(x),x)/(2*y(x)^2-x*y(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: 0.17 (sec). Leaf size: 50

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

\[ \text {Solve}\left [\int _1^{\frac {y(x)}{x}}\frac {K[1]^2-K[1]+1}{(K[1]-2) (K[1]-1) K[1]}dK[1]=-\log (x)+c_1,y(x)\right ] \]

✗ 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