Internal problem ID [9511]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 9, system of higher order odes
Problem number: 1932.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\relax (t )&=x \relax (t ) \left (y \relax (t )-z \relax (t )\right )\\ y^{\prime }\relax (t )&=y \relax (t ) \left (z \relax (t )-x \relax (t )\right )\\ z^{\prime }\relax (t )&=z \relax (t ) \left (x \relax (t )-y \relax (t )\right ) \end {align*}
✗ Solution by Maple
dsolve({diff(x(t),t)=x(t)*(y(t)-z(t)),diff(y(t),t)=y(t)*(z(t)-x(t)),diff(z(t),t)=z(t)*(x(t)-y(t))},{x(t), y(t), z(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]-z[t]),y'[t]==y[t]*(z[t]-x[t]),z'[t]==z[t]*(x[t]-y[t])},{x[t],y[t],z[t]},t,IncludeSingularSolutions -> True]
Not solved