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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 = 0.0439705 (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 = 1.076 (sec), leaf count = 704

{[{x(t)=0},{y(t)=0},{z(t)=c1}],[{x(t)=0},{y(t)=c1e2c1c2e2c1t−c1e4c1c2e4c1te2c1c2e2c1t−1,y(t)=−c1e2c1c2e2c1t−c1e4c1c2e4c1te2c1c2e2c1t−1},{z(t)=−(ddty(t))y(t)y(t),z(t)=−−(ddty(t))y(t)y(t)}],[{x(t)=c1},{y(t)=ix(t),y(t)=−ix(t)},{z(t)=ix(t),z(t)=−ix(t)}],[{x(t)=c1e2c1c2e2c1t−c1e4c1c2e4c1te2c1c2e2c1t−1,x(t)=−c1e2c1c2e2c1t−c1e4c1c2e4c1te2c1c2e2c1t−1},{y(t)=0},{z(t)=−(ddtx(t))x(t)x(t),z(t)=−−(ddtx(t))x(t)x(t)}],[{x(t)=RootOf(c3+t−(∫_Z−24_a4−16c2_a2+16c22+c1_ad_a)),x(t)=RootOf(c3+t−(∫_Z24_a4−16c2_a2+16c22+c1_ad_a))},{y(t)=−−2(x(t)3−ddtx(t)−x(t)6−(d2dt2x(t))x(t)+2(ddtx(t))2)x(t)2x(t),y(t)=−2(x(t)3−ddtx(t)−x(t)6−(d2dt2x(t))x(t)+2(ddtx(t))2)x(t)2x(t),y(t)=−−2(x(t)3−ddtx(t)+x(t)6−(d2dt2x(t))x(t)+2(ddtx(t))2)x(t)2x(t),y(t)=−2(x(t)3−ddtx(t)+x(t)6−(d2dt2x(t))x(t)+2(ddtx(t))2)x(t)2x(t)},{z(t)=(x(t)y(t)2−ddtx(t))x(t)x(t),z(t)=−(x(t)y(t)2−ddtx(t))x(t)x(t)}]}

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