14.30.4 problem 4

Internal problem ID [2817]
Book : Differential equations and their applications, 4th ed., M. Braun
Section : Chapter 4. Qualitative theory of differential equations. Section 4.3 (Stability of equilibrium solutions). Page 393
Problem number : 4
Date solved : Sunday, March 30, 2025 at 12:21:08 AM
CAS classification : system_of_ODEs

\begin{align*} \frac {d}{d t}x \left (t \right )&=6 x \left (t \right )-6 x \left (t \right )^{2}-2 x \left (t \right ) y \left (t \right )\\ \frac {d}{d t}y \left (t \right )&=4 y \left (t \right )-4 y \left (t \right )^{2}-2 x \left (t \right ) y \left (t \right ) \end{align*}

✗ Maple

ode:=[diff(x(t),t) = 6*x(t)-6*x(t)^2-2*x(t)*y(t), diff(y(t),t) = 4*y(t)-4*y(t)^2-2*x(t)*y(t)]; 
dsolve(ode);
 

\[ \text {No solution found} \]

✗ Mathematica

ode={D[x[t],t]==6*x[t]-6*x[t]^2-2*x[t]*y[t],D[y[t],t]==4*y[t]-4*y[t]^2-2*x[t]*y[t]}; 
ic={}; 
DSolve[{ode,ic},{x[t],y[t]},t,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

from sympy import * 
t = symbols("t") 
x = Function("x") 
y = Function("y") 
ode=[Eq(6*x(t)**2 + 2*x(t)*y(t) - 6*x(t) + Derivative(x(t), t),0),Eq(2*x(t)*y(t) + 4*y(t)**2 - 4*y(t) + Derivative(y(t), t),0)] 
ics = {} 
dsolve(ode,func=[x(t),y(t)],ics=ics)
 

Timed Out