54.2.246 problem 823

Internal problem ID [12120]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 823
Date solved : Wednesday, October 01, 2025 at 12:49:43 AM
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: 0.022 (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: 0.191 (sec). Leaf size: 41

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

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

✗ 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