60.2.313 problem 891

Internal problem ID [10887]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 891
Date solved : Sunday, March 30, 2025 at 07:20:11 PM
CAS classification : [_rational, [_Abel, `2nd type`, `class C`]]

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

✓ Maple. Time used: 0.005 (sec). Leaf size: 60

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

\begin{align*} y &= 0 \\ y &= \frac {x^{2}}{\sqrt {c_1 -2 \ln \left (x \right )}\, x^{2}-x^{2}+1} \\ y &= -\frac {x^{2}}{\sqrt {c_1 -2 \ln \left (x \right )}\, x^{2}+x^{2}-1} \\ \end{align*}

✓ Mathematica. Time used: 1.688 (sec). Leaf size: 106

ode=D[y[x],x] == (y[x]^2*(2*x^2 - 2*y[x] + 2*x^2*y[x] + x^4*y[x]))/(x^3*(x^2 - y[x] + x^2*y[x])); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)\to \frac {6 x^2}{6+x^2 \left (-6+\sqrt {6} \sqrt {\frac {1}{x^5}} \sqrt {x^5 (-12 \log (x)+31+6 c_1)}\right )} \\ y(x)\to -\frac {6 x^2}{-6+x^2 \left (6+\sqrt {6} \sqrt {\frac {1}{x^5}} \sqrt {x^5 (-12 \log (x)+31+6 c_1)}\right )} \\ y(x)\to 0 \\ \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(Derivative(y(x), x) - (x**4*y(x) + 2*x**2*y(x) + 2*x**2 - 2*y(x))*y(x)**2/(x**3*(x**2*y(x) + x**2 - y(x))),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out