60.2.318 problem 896

Internal problem ID [10892]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 896
Date solved : Sunday, March 30, 2025 at 07:20:32 PM
CAS classification : [_rational]

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

✓ Maple. Time used: 0.019 (sec). Leaf size: 61

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

\[ -\int _{\textit {\_b}}^{y}\frac {\textit {\_a}}{\textit {\_a}^{6}-3 \textit {\_a}^{4} x^{2}+3 \textit {\_a}^{2} x^{4}-x^{6}+\textit {\_a}^{4}-2 \textit {\_a}^{2} x^{2}+x^{4}+1}d \textit {\_a} +x -c_1 = 0 \]

✓ Mathematica. Time used: 0.235 (sec). Leaf size: 1163

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

\begin{align*} \text {Solution too large to show}\end{align*}

✗ Sympy

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

Timed Out