29.25.1 problem 698

Internal problem ID [5288]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 25
Problem number : 698
Date solved : Sunday, March 30, 2025 at 07:51:30 AM
CAS classification : [_rational]

\begin{align*} x \left (x +y+2 y^{3}\right ) y^{\prime }&=\left (x -y\right ) y \end{align*}

✓ Maple. Time used: 0.020 (sec). Leaf size: 29

ode:=x*(x+y(x)+2*y(x)^3)*diff(y(x),x) = (x-y(x))*y(x); 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.233 (sec). Leaf size: 23

ode=x(x+y[x]+2 y[x]^3)D[y[x],x]==(x-y[x])y[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x*(x + 2*y(x)**3 + y(x))*Derivative(y(x), x) - (x - y(x))*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out