ODE No. 1903

10.48 ODE No. 1903

${a \frac{d}{d t} x (t) = b c (y (t) - z (t)), b \frac{d}{d t} y (t) = c a (z (t) - x (t)), c \frac{d}{d t} z (t) = a b (x (t) - y (t))}$

Mathematica: cpu = 0.090011 (sec), leaf count = 1304 ${{x (t) \to \frac{e^{- i \sqrt{a^{2} + b^{2} + c^{2}} t} (2 e^{i \sqrt{a^{2} + b^{2} + c^{2}} t} a^{2} + b^{2} e^{2 i \sqrt{a^{2} + b^{2} + c^{2}} t} + c^{2} e^{2 i \sqrt{a^{2} + b^{2} + c^{2}} t} + b^{2} + c^{2}) c_{1}}{2 (a^{2} + b^{2} + c^{2})} - \frac{b e^{- i \sqrt{a^{2} + b^{2} + c^{2}} t} (- 1 + e^{i \sqrt{a^{2} + b^{2} + c^{2}} t}) (a e^{i \sqrt{a^{2} + b^{2} + c^{2}} t} b - a b + i c \sqrt{a^{2} + b^{2} + c^{2}} e^{i \sqrt{a^{2} + b^{2} + c^{2}} t} + i c \sqrt{a^{2} + b^{2} + c^{2}}) c_{2}}{2 a (a^{2} + b^{2} + c^{2})} - \frac{c e^{- i \sqrt{a^{2} + b^{2} + c^{2}} t} (- 1 + e^{i \sqrt{a^{2} + b^{2} + c^{2}} t}) (- i \sqrt{a^{2} + b^{2} + c^{2}} e^{i \sqrt{a^{2} + b^{2} + c^{2}} t} b - i \sqrt{a^{2} + b^{2} + c^{2}} b + a c e^{i \sqrt{a^{2} + b^{2} + c^{2}} t} - a c) c_{3}}{2 a (a^{2} + b^{2} + c^{2})}, y (t) \to - \frac{a e^{- i \sqrt{a^{2} + b^{2} + c^{2}} t} (- 1 + e^{i \sqrt{a^{2} + b^{2} + c^{2}} t}) (a e^{i \sqrt{a^{2} + b^{2} + c^{2}} t} b - a b - i c \sqrt{a^{2} + b^{2} + c^{2}} e^{i \sqrt{a^{2} + b^{2} + c^{2}} t} - i c \sqrt{a^{2} + b^{2} + c^{2}}) c_{1}}{2 b (a^{2} + b^{2} + c^{2})} + \frac{e^{- i \sqrt{a^{2} + b^{2} + c^{2}} t} (e^{2 i \sqrt{a^{2} + b^{2} + c^{2}} t} a^{2} + a^{2} + 2 b^{2} e^{i \sqrt{a^{2} + b^{2} + c^{2}} t} + c^{2} e^{2 i \sqrt{a^{2} + b^{2} + c^{2}} t} + c^{2}) c_{2}}{2 (a^{2} + b^{2} + c^{2})} - \frac{c e^{- i \sqrt{a^{2} + b^{2} + c^{2}} t} (- 1 + e^{i \sqrt{a^{2} + b^{2} + c^{2}} t}) (i \sqrt{a^{2} + b^{2} + c^{2}} e^{i \sqrt{a^{2} + b^{2} + c^{2}} t} a + i \sqrt{a^{2} + b^{2} + c^{2}} a + b c e^{i \sqrt{a^{2} + b^{2} + c^{2}} t} - b c) c_{3}}{2 b (a^{2} + b^{2} + c^{2})}, z (t) \to - \frac{a e^{- i \sqrt{a^{2} + b^{2} + c^{2}} t} (- 1 + e^{i \sqrt{a^{2} + b^{2} + c^{2}} t}) (i \sqrt{a^{2} + b^{2} + c^{2}} e^{i \sqrt{a^{2} + b^{2} + c^{2}} t} b + i \sqrt{a^{2} + b^{2} + c^{2}} b + a c e^{i \sqrt{a^{2} + b^{2} + c^{2}} t} - a c) c_{1}}{2 c (a^{2} + b^{2} + c^{2})} - \frac{b e^{- i \sqrt{a^{2} + b^{2} + c^{2}} t} (- 1 + e^{i \sqrt{a^{2} + b^{2} + c^{2}} t}) (- i \sqrt{a^{2} + b^{2} + c^{2}} e^{i \sqrt{a^{2} + b^{2} + c^{2}} t} a - i \sqrt{a^{2} + b^{2} + c^{2}} a + b c e^{i \sqrt{a^{2} + b^{2} + c^{2}} t} - b c) c_{2}}{2 c (a^{2} + b^{2} + c^{2})} + \frac{e^{- i \sqrt{a^{2} + b^{2} + c^{2}} t} (e^{2 i \sqrt{a^{2} + b^{2} + c^{2}} t} a^{2} + a^{2} + 2 c^{2} e^{i \sqrt{a^{2} + b^{2} + c^{2}} t} + b^{2} e^{2 i \sqrt{a^{2} + b^{2} + c^{2}} t} + b^{2}) c_{3}}{2 (a^{2} + b^{2} + c^{2})}}}$

Maple: cpu = 0.109 (sec), leaf count = 312 ${{x (t) =_C 1 +_C 2 \sin (\sqrt{a^{2} + b^{2} + c^{2}} t) +_C 3 \cos (\sqrt{a^{2} + b^{2} + c^{2}} t), y (t) = - \frac{1}{b (b^{2} + c^{2})} (\sin (\sqrt{a^{2} + b^{2} + c^{2}} t) \sqrt{a^{2} + b^{2} + c^{2}}_C 3 a c + \sin (\sqrt{a^{2} + b^{2} + c^{2}} t)_C 2 a^{2} b - \cos (\sqrt{a^{2} + b^{2} + c^{2}} t) \sqrt{a^{2} + b^{2} + c^{2}}_C 2 a c + \cos (\sqrt{a^{2} + b^{2} + c^{2}} t)_C 3 a^{2} b -_C 1 b^{3} -_C 1 b c^{2}), z (t) = \frac{1}{(b^{2} + c^{2}) c} (\sin (\sqrt{a^{2} + b^{2} + c^{2}} t) \sqrt{a^{2} + b^{2} + c^{2}}_C 3 a b - \sin (\sqrt{a^{2} + b^{2} + c^{2}} t)_C 2 a^{2} c - \cos (\sqrt{a^{2} + b^{2} + c^{2}} t) \sqrt{a^{2} + b^{2} + c^{2}}_C 2 a b - \cos (\sqrt{a^{2} + b^{2} + c^{2}} t)_C 3 a^{2} c +_C 1 b^{2} c +_C 1 c^{3})}}$

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