80.11.24 problem 25

Internal problem ID [21432]
Book : A Textbook on Ordinary Differential Equations by Shair Ahmad and Antonio Ambrosetti. Second edition. ISBN 978-3-319-16407-6. Springer 2015
Section : Chapter 12. Stability theory. Excercise 12.6 at page 270
Problem number : 25
Date solved : Thursday, October 02, 2025 at 07:31:31 PM
CAS classification : system_of_ODEs

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

✗ Maple

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

\[ \text {No solution found} \]

✗ Mathematica

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

Timed Out