54.10.8 problem 1920

Internal problem ID [13142]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 9, system of higher order odes
Problem number : 1920
Date solved : Wednesday, October 01, 2025 at 03:36:40 AM
CAS classification : system_of_ODEs

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

✗ Maple

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

\[ \text {No solution found} \]

✗ Mathematica

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

Timed Out