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

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

✗ Solution by Maple

dsolve([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)],singsol=all)
 

\[ \text {No solution found} \]

✗ Solution by Mathematica

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

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

Not solved