14.30.1 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 : Monday, January 27, 2025 at 06:14:13 AM
CAS classification : system_of_ODEs

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

✗ Solution by Maple

dsolve([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],singsol=all)
 

\[ \text {No solution found} \]

✗ Solution by Mathematica

Time used: 0.000 (sec). Leaf size: 0

DSolve[{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},{x[t],y[t]},t,IncludeSingularSolutions -> True]
 

Not solved