60.1.252 problem 257

Internal problem ID [10266]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 257
Date solved : Sunday, March 30, 2025 at 03:35:24 PM
CAS classification : [_rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} x \left (x y+x^{4}-1\right ) y^{\prime }-y \left (x y-x^{4}-1\right )&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 57

ode:=x*(x*y(x)+x^4-1)*diff(y(x),x)-y(x)*(x*y(x)-x^4-1) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {-{\mathrm e}^{-\operatorname {RootOf}\left (-2 \textit {\_Z} \,x^{4} {\mathrm e}^{2 \textit {\_Z}}+2 x^{4} {\mathrm e}^{2 \textit {\_Z}}-2 \,{\mathrm e}^{\textit {\_Z}} c_1 \,x^{4}+{\mathrm e}^{2 \textit {\_Z}}-2 \,{\mathrm e}^{\textit {\_Z}} c_1 +c_1^{2}\right )} c_1 +1}{x} \]

✓ Mathematica. Time used: 0.292 (sec). Leaf size: 39

ode=x*(x*y[x]+x^4-1)*D[y[x],x]-y[x]*(x*y[x]-x^4-1)==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✗ Sympy

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

Timed Out