60.1.290 problem 296

Internal problem ID [10304]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 296
Date solved : Sunday, March 30, 2025 at 03:57:37 PM
CAS classification : [_rational, [_1st_order, `_with_symmetry_[F(x),G(x)*y+H(x)]`]]

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

✓ Maple. Time used: 0.058 (sec). Leaf size: 51

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

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

✓ Mathematica. Time used: 0.793 (sec). Leaf size: 88

ode=x*(y[x]^2+x^2*y[x]+x^2)*D[y[x],x]-2*y[x]^3-2*x^2*y[x]^2+x^4==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)\to -e^{-c_1} \left (x^2+\sqrt {x^2 \left (x^2-e^{c_1} x^2+e^{2 c_1}\right )}\right ) \\ y(x)\to e^{-c_1} \left (-x^2+\sqrt {x^2 \left (x^2-e^{c_1} x^2+e^{2 c_1}\right )}\right ) \\ \end{align*}

✗ Sympy

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

Timed Out