76.10.17 problem 17

Internal problem ID [17539]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 3. Systems of two first order equations. Section 3.6 (A brief introduction to nonlinear systems). Problems at page 195
Problem number : 17
Date solved : Tuesday, January 28, 2025 at 10:40:04 AM
CAS classification : system_of_ODEs

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

✗ Solution by Maple

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

Not solved