Internal problem ID [9498]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 9, system of higher order odes
Problem number: 1919.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\relax (t )&=x \relax (t )+y \relax (t )-x \relax (t ) \left (x \relax (t )^{2}+y \relax (t )^{2}\right )\\ y^{\prime }\relax (t )&=-x \relax (t )+y \relax (t )-y \relax (t ) \left (x \relax (t )^{2}+y \relax (t )^{2}\right ) \end {align*}
✗ Solution by Maple
dsolve({diff(x(t),t)=x(t)+y(t)-x(t)*(x(t)^2+y(t)^2),diff(y(t),t)=-x(t)+y(t)-y(t)*(x(t)^2+y(t)^2)},{x(t), y(t)}, singsol=all)
\[ \text {No solution found} \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[{x'[t]==x[t]+y[t]-x[t]*(x[t]^2+y[t]^2),y'[t]==-x[t]+y[t]-y[t]*(x[t]^2+y[t]^2)},{x[t],y[t]},t,IncludeSingularSolutions -> True]
Not solved