14.27.1 problem 1

Internal problem ID [2789]
Book : Differential equations and their applications, 4th ed., M. Braun
Section : Chapter 4. Qualitative theory of differential equations. Section 4.1 (Introduction). Page 3770
Problem number : 1
Date solved : Monday, January 27, 2025 at 06:13:52 AM
CAS classification : system_of_ODEs

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

✗ Solution by Maple

dsolve([diff(x(t),t)=x(t)-x(t)^2-2*x(t)*y(t),diff(y(t),t)=2*y(t)-2*y(t)^2-3*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]==x[t]-x[t]^2-2*x[t]*y[t],D[y[t],t]==2*y[t]-2*y[t]^2-3*x[t]*y[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
 

Not solved