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2.1936   ODE No. 1936

  1. Problem in Latex
  2. Mathematica input
  3. Maple input

{x′(t)=x(t)(y(t)2−z(t)2),y′(t)=−y(t)(x(t)2+z(t)2),z′(t)=z(t)(x(t)2+y(t)2)} ✗ Mathematica : cpu = 0.0566234 (sec), leaf count = 0 , 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 = 0.791 (sec), leaf count = 704

{[{x(t)=0},{y(t)=0},{z(t)=_C1}],[{x(t)=0},{y(t)=1(e_C2_C1)2(e_C1t)2−1−(e_C1t)4_C1(e_C2_C1)4+(e_C1t)2_C1(e_C2_C1)2,y(t)=−1(e_C2_C1)2(e_C1t)2−1−(e_C1t)4_C1(e_C2_C1)4+(e_C1t)2_C1(e_C2_C1)2},{z(t)=1y(t)−y(t)ddty(t),z(t)=−1y(t)−y(t)ddty(t)}],[{x(t)=_C1},{y(t)=−ix(t),y(t)=ix(t)},{z(t)=−ix(t),z(t)=ix(t)}],[{x(t)=1(e_C2_C1)2(e_C1t)2−1−(e_C1t)4_C1(e_C2_C1)4+(e_C1t)2_C1(e_C2_C1)2,x(t)=−1(e_C2_C1)2(e_C1t)2−1−(e_C1t)4_C1(e_C2_C1)4+(e_C1t)2_C1(e_C2_C1)2},{y(t)=0},{z(t)=1x(t)−x(t)ddtx(t),z(t)=−1x(t)−x(t)ddtx(t)}],[{x(t)=RootOf(−∫_Z−214_a4−16_C2_a2+16_C22+_C1_ad_a+t+_C3),x(t)=RootOf(−∫_Z214_a4−16_C2_a2+16_C22+_C1_ad_a+t+_C3)},{y(t)=−12x(t)−2x(t)((x(t))3−ddtx(t)−(x(t))6−(d2dt2x(t))x(t)+2(ddtx(t))2),y(t)=12x(t)−2x(t)((x(t))3−ddtx(t)−(x(t))6−(d2dt2x(t))x(t)+2(ddtx(t))2),y(t)=−12x(t)−2x(t)((x(t))3−ddtx(t)+(x(t))6−(d2dt2x(t))x(t)+2(ddtx(t))2),y(t)=12x(t)−2x(t)((x(t))3−ddtx(t)+(x(t))6−(d2dt2x(t))x(t)+2(ddtx(t))2)},{z(t)=1x(t)x(t)(x(t)(y(t))2−ddtx(t)),z(t)=−1x(t)x(t)(x(t)(y(t))2−ddtx(t))}]}

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