76.10.22 problem 25

Internal problem ID [17465]
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 : 25
Date solved : Thursday, March 13, 2025 at 10:08:56 AM
CAS classification : system_of_ODEs

\begin{align*} \frac {d}{d t}x \left (t \right )&=x \left (t \right ) \left (1-x \left (t \right )-y \left (t \right )\right )\\ \frac {d}{d t}y \left (t \right )&=y \left (t \right ) \left (\frac {3}{4}-y \left (t \right )-\frac {x \left (t \right )}{2}\right ) \end{align*}

✗ Maple

ode:=[diff(x(t),t) = x(t)*(1-x(t)-y(t)), diff(y(t),t) = y(t)*(3/4-y(t)-1/2*x(t))]; 
dsolve(ode);
 

\[ \text {No solution found} \]

✗ Mathematica

ode={D[x[t],t]==x[t]*(1-x[t]-y[t]),D[y[t],t]==y[t]*(75/100-y[t]-1/2*x[t])}; 
ic={}; 
DSolve[{ode,ic},{x[t],y[t]},t,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

from sympy import * 
t = symbols("t") 
x = Function("x") 
y = Function("y") 
ode=[Eq((x(t) + y(t) - 1)*x(t) + Derivative(x(t), t),0),Eq((x(t)/2 + y(t) - 3/4)*y(t) + Derivative(y(t), t),0)] 
ics = {} 
dsolve(ode,func=[x(t),y(t)],ics=ics)
 

Timed Out