Internal problem ID [9495]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 9, system of higher order odes
Problem number: 1920.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=-y \left (t \right )+x \left (t \right ) \left (x \left (t \right )^{2}+y \left (t \right )^{2}-1\right )\\ y^{\prime }\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)],[x(t), y(t)], singsol=all)
\[ \text {No solution found} \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[{x'[t]==-y[t]+x[t]*(x[t]^2+y[t]^2-1),y'[t]==x[t]+y[t]*(x[t]^2+y[t]^2-1)},{x[t],y[t]},t,IncludeSingularSolutions -> True]
Not solved