14.27.2 problem 2

Internal problem ID [2790]
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 : 2
Date solved : Sunday, March 30, 2025 at 12:20:33 AM
CAS classification : system_of_ODEs

\begin{align*} \frac {d}{d t}x \left (t \right )&=-b x \left (t \right ) y \left (t \right )+m\\ \frac {d}{d t}y \left (t \right )&=b x \left (t \right ) y \left (t \right )-g y \left (t \right ) \end{align*}

✗ Maple

ode:=[diff(x(t),t) = -b*x(t)*y(t)+m, diff(y(t),t) = b*x(t)*y(t)-g*y(t)]; 
dsolve(ode);
 

\[ \text {No solution found} \]

✗ Mathematica

ode={D[x[t],t]==-b*x[t]*y[t]+m,D[y[t],t]==b*x[t]*y[t]-g*y[t]}; 
ic={}; 
DSolve[{ode,ic},{x[t],y[t]},t,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

from sympy import * 
t = symbols("t") 
b = symbols("b") 
g = symbols("g") 
m = symbols("m") 
x = Function("x") 
y = Function("y") 
ode=[Eq(b*x(t)*y(t) - m + Derivative(x(t), t),0),Eq(-b*x(t)*y(t) + g*y(t) + Derivative(y(t), t),0)] 
ics = {} 
dsolve(ode,func=[x(t),y(t)],ics=ics)
 

Timed Out