73.28.4 problem 39.1 (d)

Internal problem ID [15708]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 39. Critical points, Direction fields and trajectories. Additional Exercises. page 815
Problem number : 39.1 (d)
Date solved : Monday, March 31, 2025 at 01:45:41 PM
CAS classification : system_of_ODEs

\begin{align*} \frac {d}{d t}x \left (t \right )&=x \left (t \right ) y \left (t \right )-6 y \left (t \right )\\ \frac {d}{d t}y \left (t \right )&=x \left (t \right )-y \left (t \right )-5 \end{align*}

✗ Maple

ode:=[diff(x(t),t) = x(t)*y(t)-6*y(t), diff(y(t),t) = x(t)-y(t)-5]; 
dsolve(ode);
 

\[ \text {No solution found} \]

✗ Mathematica

ode={D[x[t],t]==x[t]*y[t]-6*y[t],D[y[t],t]==x[t]-y[t]-5}; 
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) + 6*y(t) + Derivative(x(t), t),0),Eq(-x(t) + y(t) + Derivative(y(t), t) + 5,0)] 
ics = {} 
dsolve(ode,func=[x(t),y(t)],ics=ics)
 

Timed Out