60.2.254 problem 830

Internal problem ID [10828]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 830
Date solved : Sunday, March 30, 2025 at 07:10:36 PM
CAS classification : [_rational]

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

✓ Maple. Time used: 0.026 (sec). Leaf size: 38

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

\[ y = {\mathrm e}^{\operatorname {RootOf}\left (2 \,{\mathrm e}^{4 \textit {\_Z}}+3 \,{\mathrm e}^{3 \textit {\_Z}}-6 \ln \left (x \right ) {\mathrm e}^{\textit {\_Z}}+6 c_1 \,{\mathrm e}^{\textit {\_Z}}+6 \textit {\_Z} \,{\mathrm e}^{\textit {\_Z}}+6 x \right )} \]

✓ Mathematica. Time used: 0.308 (sec). Leaf size: 38

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

\[ \text {Solve}\left [-\frac {1}{3} y(x)^3-\frac {y(x)^2}{2}-\frac {x}{y(x)}-\log (y(x))+\log (x)-1=c_1,y(x)\right ] \]

✗ Sympy

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

Timed Out