Internal problem ID [10267]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 9, system of higher order odes
Problem number: 1935.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=-z \left (t \right )^{2} x \left (t \right )+x \left (t \right ) y \left (t \right )^{2}\\ y^{\prime }\left (t \right )&=z \left (t \right )^{2} y \left (t \right )-x \left (t \right )^{2} y \left (t \right )\\ z^{\prime }\left (t \right )&=z \left (t \right ) x \left (t \right )^{2}-z \left (t \right ) y \left (t \right )^{2} \end {align*}
✗ Solution by Maple
dsolve([diff(x(t),t)=x(t)*(y(t)^2-z(t)^2),diff(y(t),t)=y(t)*(z(t)^2-x(t)^2),diff(z(t),t)=z(t)*(x(t)^2-y(t)^2)],[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]^2-z[t]^2),y'[t]==y[t]*(z[t]^2-x[t]^2),z'[t]==z[t]*(x[t]^2-y[t]^2)},{x[t],y[t],z[t]},t,IncludeSingularSolutions -> True]
Not solved