87.30.13 problem 13

Internal problem ID [23912]
Book : Ordinary differential equations with modern applications. Ladas, G. E. and Finizio, N. Wadsworth Publishing. California. 1978. ISBN 0-534-00552-7. QA372.F56
Section : Chapter 8. Nonlinear differential equations and systems. Exercise at page 310
Problem number : 13
Date solved : Thursday, October 02, 2025 at 09:46:29 PM
CAS classification : system_of_ODEs

\begin{align*} \frac {d}{d t}x \left (t \right )&=5 x \left (t \right )-6 y \left (t \right )+x \left (t \right ) y \left (t \right )\\ \frac {d}{d t}y \left (t \right )&=6 x \left (t \right )-7 y \left (t \right )-x \left (t \right ) y \left (t \right ) \end{align*}

✗ Maple

ode:=[diff(x(t),t) = 5*x(t)-6*y(t)+x(t)*y(t), diff(y(t),t) = 6*x(t)-7*y(t)-x(t)*y(t)]; 
dsolve(ode);
 

\[ \text {No solution found} \]

✗ Mathematica

ode={D[x[t],t]==5*x[t]-6*y[t]+x[t]*y[t],D[y[t],t]==6*x[t]-7*y[t]-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)*y(t) - 5*x(t) + 6*y(t) + Derivative(x(t), t),0),Eq(x(t)*y(t) - 6*x(t) + 7*y(t) + Derivative(y(t), t),0)] 
ics = {} 
dsolve(ode,func=[x(t),y(t)],ics=ics)
 

Timed Out