70.10.18 problem 18

Internal problem ID [18827]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 3. Systems of two first order equations. Section 3.6 (A brief introduction to nonlinear systems). Problems at page 195
Problem number : 18
Date solved : Thursday, October 02, 2025 at 03:31:12 PM
CAS classification : system_of_ODEs

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

✗ Maple

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

\[ \text {No solution found} \]

✗ Mathematica

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

Timed Out