54.2.327 problem 906

Internal problem ID [12201]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 906
Date solved : Wednesday, October 01, 2025 at 01:08:45 AM
CAS classification : [_rational]

\begin{align*} y^{\prime }&=\frac {x \left (x^{2}+y^{2}+1\right )}{-y^{3}-x^{2} y-y+y^{6}+3 x^{2} y^{4}+3 x^{4} y^{2}+x^{6}} \end{align*}

✓ Maple. Time used: 0.099 (sec). Leaf size: 37

ode:=diff(y(x),x) = x*(x^2+y(x)^2+1)/(-y(x)^3-x^2*y(x)-y(x)+y(x)^6+3*y(x)^4*x^2+3*x^4*y(x)^2+x^6); 
dsolve(ode,y(x), singsol=all);
 

\[ -\frac {1}{4 \left (x^{2}+y^{2}\right )^{2}}-\frac {1}{2 x^{2}+2 y^{2}}-y+c_1 = 0 \]

✓ Mathematica. Time used: 0.102 (sec). Leaf size: 127

ode=D[y[x],x] == (x*(1 + x^2 + y[x]^2))/(x^6 - y[x] - x^2*y[x] + 3*x^4*y[x]^2 - y[x]^3 + 3*x^2*y[x]^4 + y[x]^6); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ \text {Solve}\left [\int _1^{y(x)}\left (-\frac {K[2]}{\left (x^2+K[2]^2\right )^2}-\frac {K[2]}{\left (x^2+K[2]^2\right )^3}-\int _1^x\left (\frac {4 K[1] K[2]}{\left (K[1]^2+K[2]^2\right )^3}+\frac {6 K[1] K[2]}{\left (K[1]^2+K[2]^2\right )^4}\right )dK[1]+1\right )dK[2]+\int _1^x\left (-\frac {K[1]}{\left (K[1]^2+y(x)^2\right )^2}-\frac {K[1]}{\left (K[1]^2+y(x)^2\right )^3}\right )dK[1]=c_1,y(x)\right ] \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x*(x**2 + y(x)**2 + 1)/(x**6 + 3*x**4*y(x)**2 + 3*x**2*y(x)**4 - x**2*y(x) + y(x)**6 - y(x)**3 - y(x)) + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out