60.1.260 problem 265

Internal problem ID [10274]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 265
Date solved : Sunday, March 30, 2025 at 03:36:30 PM
CAS classification : [_rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} \left (x^{n \left (n +1\right )} y-1\right ) y^{\prime }+2 \left (n +1\right )^{2} x^{n -1} \left (x^{n^{2}} y^{2}-1\right )&=0 \end{align*}

✗ Maple

ode:=(x^(n*(n+1))*y(x)-1)*diff(y(x),x)+2*(n+1)^2*x^(n-1)*(x^(n^2)*y(x)^2-1) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=(x^(n*(n+1))*y[x]-1)*D[y[x],x]+2*(n+1)^2*x^(n-1)*(x^(n^2)*y[x]^2-1)==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

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

Timed Out