60.1.518 problem 531

Internal problem ID [10532]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 531
Date solved : Sunday, March 30, 2025 at 05:47:46 PM
CAS classification : [`y=_G(x,y')`]

\begin{align*} {y^{\prime }}^{2}-\left (y^{4}+x y^{2}+x^{2}\right ) {y^{\prime }}^{2}+\left (x y^{6}+x^{2} y^{4}+x^{3} y^{2}\right ) y^{\prime }-x^{3} y^{6}&=0 \end{align*}

✗ Maple

ode:=diff(y(x),x)^2-(y(x)^4+x*y(x)^2+x^2)*diff(y(x),x)^2+(x*y(x)^6+x^2*y(x)^4+x^3*y(x)^2)*diff(y(x),x)-x^3*y(x)^6 = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=-(x^3*y[x]^6) + (x^3*y[x]^2 + x^2*y[x]^4 + x*y[x]^6)*D[y[x],x] + D[y[x],x]^2 - (x^2 + x*y[x]^2 + y[x]^4)*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(-x**3*y(x)**6 - (x**2 + x*y(x)**2 + y(x)**4)*Derivative(y(x), x)**2 + (x**3*y(x)**2 + x**2*y(x)**4 + x*y(x)**6)*Derivative(y(x), x) + Derivative(y(x), x)**2,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out