82.8.24 problem 36-25

Internal problem ID [21895]
Book : The Differential Equations Problem Solver. VOL. II. M. Fogiel director. REA, NY. 1978. ISBN 78-63609
Section : Chapter 36. Nonlinear differential equations. Page 1203
Problem number : 36-25
Date solved : Thursday, October 02, 2025 at 08:05:50 PM
CAS classification : system_of_ODEs

\begin{align*} \frac {d}{d t}x \left (t \right )&=x \left (t \right )+4 y \left (t \right )-y \left (t \right )^{2}\\ \frac {d}{d t}y \left (t \right )&=6 x \left (t \right )-y \left (t \right )+2 x \left (t \right ) y \left (t \right ) \end{align*}

✗ Maple

ode:=[diff(x(t),t) = x(t)+4*y(t)-y(t)^2, diff(y(t),t) = 6*x(t)-y(t)+2*x(t)*y(t)]; 
dsolve(ode);
 

\[ \text {No solution found} \]

✗ Mathematica

ode={D[x[t],t]==x[t]+4*y[t]-y[t]^2,D[y[t],t]==6*x[t]-y[t]+2*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) - 4*y(t)**2 + Derivative(x(t), t),0),Eq(-2*x(t)*y(t) - 6*x(t) + y(t) + Derivative(y(t), t),0)] 
ics = {} 
dsolve(ode,func=[x(t),y(t)],ics=ics)
 

Timed Out