2.1936   ODE No. 1936

\[ \left \{x'(t)=x(t) \left (y(t)^2-z(t)^2\right ),y'(t)=-y(t) \left (x(t)^2+z(t)^2\right ),z'(t)=z(t) \left (x(t)^2+y(t)^2\right )\right \} \]

✗ Mathematica : cpu = 0.0389329 (sec), leaf count = 0

DSolve[{Derivative[1][x][t] == x[t]*(y[t]^2 - z[t]^2), Derivative[1][y][t] == -(y[t]*(x[t]^2 + z[t]^2)), Derivative[1][z][t] == (x[t]^2 + y[t]^2)*z[t]},{x[t], y[t], z[t]},t]
 

, could not solve

DSolve[{Derivative[1][x][t] == x[t]*(y[t]^2 - z[t]^2), Derivative[1][y][t] == -(y[t]*(x[t]^2 + z[t]^2)), Derivative[1][z][t] == (x[t]^2 + y[t]^2)*z[t]}, {x[t], y[t], z[t]}, t]

✓ Maple : cpu = 0.772 (sec), leaf count = 704

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)})
 

\[[\{x \left (t \right ) = 0\}, \{y \left (t \right ) = 0\}, \{z \left (t \right ) = c_{1}\}]\]