60.1.493 problem 506

Internal problem ID [10507]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 506
Date solved : Sunday, March 30, 2025 at 05:31:03 PM
CAS classification : [`y=_G(x,y')`]

\begin{align*} x^{2} \left (x y^{2}-1\right ) {y^{\prime }}^{2}+2 x^{2} y^{2} \left (y-x \right ) y^{\prime }-y^{2} \left (x^{2} y-1\right )&=0 \end{align*}

✗ Maple

ode:=x^2*(-1+x*y(x)^2)*diff(y(x),x)^2+2*x^2*y(x)^2*(y(x)-x)*diff(y(x),x)-y(x)^2*(x^2*y(x)-1) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=-(y[x]^2*(-1 + x^2*y[x])) + 2*x^2*y[x]^2*(-x + y[x])*D[y[x],x] + x^2*(-1 + x*y[x]^2)*D[y[x],x]^2==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

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

Timed Out