54.2.244 problem 821

Internal problem ID [12118]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 821
Date solved : Wednesday, October 01, 2025 at 12:46:04 AM
CAS classification : [_rational]

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

✓ Maple. Time used: 0.013 (sec). Leaf size: 27

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

\[ -\frac {1}{2 y^{2} x^{2}}-\frac {1}{3 y^{3} x^{3}}-y+c_1 = 0 \]

✓ Mathematica. Time used: 60.114 (sec). Leaf size: 1993

ode=D[y[x],x] == (y[x]*(1 + x*y[x]))/(x*(-1 - x*y[x] + x^3*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) - (x*y(x) + 1)*y(x)/(x*(x**3*y(x)**4 - x*y(x) - 1)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out