60.2.194 problem 770

Internal problem ID [10768]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 770
Date solved : Sunday, March 30, 2025 at 06:36:04 PM
CAS classification : [_rational]

\begin{align*} y^{\prime }&=\frac {2 y^{6}}{y^{3}+2+16 x y^{2}+32 x^{2} y^{4}} \end{align*}

✓ Maple. Time used: 0.005 (sec). Leaf size: 775

ode:=diff(y(x),x) = 2*y(x)^6/(y(x)^3+2+16*x*y(x)^2+32*x^2*y(x)^4); 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 19.606 (sec). Leaf size: 952

ode=D[y[x],x] == (2*y[x]^6)/(2 + 16*x*y[x]^2 + y[x]^3 + 32*x^2*y[x]^4); 
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(Derivative(y(x), x) - 2*y(x)**6/(32*x**2*y(x)**4 + 16*x*y(x)**2 + y(x)**3 + 2),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out