8.30.1 problem 1

Internal problem ID [2814]
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 : 1
Date solved : Tuesday, September 30, 2025 at 05:52:57 AM
CAS classification : system_of_ODEs

\begin{align*} \frac {d}{d t}x \left (t \right )&=x \left (t \right )-x \left (t \right )^{3}-x \left (t \right ) y \left (t \right )\\ \frac {d}{d t}y \left (t \right )&=2 y \left (t \right )-y \left (t \right )^{5}-y \left (t \right ) x \left (t \right )^{4} \end{align*}

✗ Maple

ode:=[diff(x(t),t) = x(t)-x(t)^3-x(t)*y(t), diff(y(t),t) = 2*y(t)-y(t)^5-y(t)*x(t)^4]; 
dsolve(ode);
 

\[ \text {No solution found} \]

✗ Mathematica

ode={D[x[t],t]==x[t]-x[t]^3-x[t]*y[t],D[y[t],t]==2*y[t]-y[t]^5-y[t]*x[t]^4}; 
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(x(t)**3 + x(t)*y(t) - x(t) + Derivative(x(t), t),0),Eq(x(t)**4*y(t) + y(t)**5 - 2*y(t) + Derivative(y(t), t),0)] 
ics = {} 
dsolve(ode,func=[x(t),y(t)],ics=ics)
 

Timed Out