87.31.17 problem 17

Internal problem ID [23933]
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 321
Problem number : 17
Date solved : Thursday, October 02, 2025 at 09:46:37 PM
CAS classification : system_of_ODEs

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

✗ Maple

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

\[ \text {No solution found} \]

✗ Mathematica

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

Timed Out