14.30.2 problem 2

Internal problem ID [2815]
Book : Differential equations and their applications, 4th ed., M. Braun
Section : Chapter 4. Qualitative theory of differential equations. Section 4.3 (Stability of equilibrium solutions). Page 393
Problem number : 2
Date solved : Sunday, March 30, 2025 at 12:21:06 AM
CAS classification : system_of_ODEs

\begin{align*} \frac {d}{d t}x \left (t \right )&=x \left (t \right )^{2}+y \left (t \right )^{2}+1\\ \frac {d}{d t}y \left (t \right )&=x \left (t \right )^{2}-y \left (t \right )^{2} \end{align*}

✗ Maple

ode:=[diff(x(t),t) = x(t)^2+y(t)^2+1, diff(y(t),t) = x(t)^2-y(t)^2]; 
dsolve(ode);
 

\[ \text {No solution found} \]

✗ Mathematica

ode={D[x[t],t]==x[t]^2+y[t]^2+1,D[y[t],t]==x[t]^2-y[t]^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)**2 - y(t)**2 + Derivative(x(t), t) - 1,0),Eq(-x(t)**2 + y(t)**2 + Derivative(y(t), t),0)] 
ics = {} 
dsolve(ode,func=[x(t),y(t)],ics=ics)
 

Timed Out