76.10.15 problem 15

Internal problem ID [17466]
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 : Monday, March 31, 2025 at 04:14:25 PM
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*}

✗ Maple

ode:=[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)]; 
dsolve(ode);
 

\[ \text {No solution found} \]

✗ Mathematica

ode={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]}; 
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)**2 + x(t)*y(t) - x(t) + Derivative(x(t), t),0),Eq(3*x(t)*y(t)/4 + y(t)**2/4 - y(t)/2 + Derivative(y(t), t),0)] 
ics = {} 
dsolve(ode,func=[x(t),y(t)],ics=ics)
 

Timed Out