60.10.8 problem 1920

Internal problem ID [11919]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 9, system of higher order odes
Problem number : 1920
Date solved : Monday, January 27, 2025 at 11:47:20 PM
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*}

✗ Solution by Maple

dsolve([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)],singsol=all)
 

\[ \text {No solution found} \]

✗ Solution by Mathematica

Time used: 0.000 (sec). Leaf size: 0

DSolve[{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)},{x[t],y[t]},t,IncludeSingularSolutions -> True]
 

Not solved