76.10.15 problem 15

Internal problem ID [17537]
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 : 15
Date solved : Tuesday, January 28, 2025 at 10:40:03 AM
CAS classification : system_of_ODEs

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

✗ Solution by Maple

dsolve([diff(x(t),t)=x(t)-x(t)^2-x(t)*y(t),diff(y(t),t)=1/2*y(t)-1/4*y(t)^2-3/4*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-x[t]*y[t],D[y[t],t]==1/2*y[t]-1/4*y[t]^2-3/4*x[t]*y[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
 

Not solved