\[ \boxed { \left \{ a{\frac {\rm d}{{\rm d}t}}x \left ( t \right ) = \left ( b-c \right ) y \left ( t \right ) z \left ( t \right ) ,b{\frac {\rm d}{{\rm d}t}}y \left ( t \right ) = \left ( c-a \right ) z \left ( t \right ) x \left ( t \right ) ,c{\frac {\rm d}{{\rm d}t}}z \left ( t \right ) = \left ( a-b \right ) x \left ( t \right ) y \left ( t \right ) \right \} } \]
Mathematica: cpu = 6.037767 (sec), leaf count = 10101 \[ \left \{\left \{x(t)\to \frac {\frac {\sqrt {2} b^2 \sqrt {a (a-c)} c_1 \text {sn}\left (\frac {\frac {\sqrt {2} \sqrt {a} \sqrt {a-c} c \sqrt {c_2} t}{\sqrt {b} \sqrt {b-c}}-\frac {\sqrt {2} \sqrt {a} \sqrt {b} \sqrt {a-c} \sqrt {c_2} t}{\sqrt {b-c}}-\frac {\sqrt {2} \sqrt {a} \sqrt {a-c} c \sqrt {c_2} c_3}{\sqrt {b} \sqrt {b-c}}+\frac {\sqrt {2} \sqrt {a} \sqrt {b} \sqrt {a-c} \sqrt {c_2} c_3}{\sqrt {b-c}}}{a}|-\frac {(a-b) b c_1}{(a-c) c c_2}\right )}{(a-c) \sqrt {b (b-c) c_1}}-\frac {\sqrt {2} b \sqrt {a (a-c)} c c_1 \text {sn}\left (\frac {\frac {\sqrt {2} \sqrt {a} \sqrt {a-c} c \sqrt {c_2} t}{\sqrt {b} \sqrt {b-c}}-\frac {\sqrt {2} \sqrt {a} \sqrt {b} \sqrt {a-c} \sqrt {c_2} t}{\sqrt {b-c}}-\frac {\sqrt {2} \sqrt {a} \sqrt {a-c} c \sqrt {c_2} c_3}{\sqrt {b} \sqrt {b-c}}+\frac {\sqrt {2} \sqrt {a} \sqrt {b} \sqrt {a-c} \sqrt {c_2} c_3}{\sqrt {b-c}}}{a}|-\frac {(a-b) b c_1}{(a-c) c c_2}\right )}{(a-c) \sqrt {b (b-c) c_1}}}{a},y(t)\to -\frac {\sqrt {2 c_1 b^2-2 c c_1 b+\frac {c \left (\frac {\sqrt {2} b^2 \sqrt {a (a-c)} c_1 \text {sn}\left (\frac {\frac {\sqrt {2} \sqrt {a} \sqrt {a-c} c \sqrt {c_2} t}{\sqrt {b} \sqrt {b-c}}-\frac {\sqrt {2} \sqrt {a} \sqrt {b} \sqrt {a-c} \sqrt {c_2} t}{\sqrt {b-c}}-\frac {\sqrt {2} \sqrt {a} \sqrt {a-c} c \sqrt {c_2} c_3}{\sqrt {b} \sqrt {b-c}}+\frac {\sqrt {2} \sqrt {a} \sqrt {b} \sqrt {a-c} \sqrt {c_2} c_3}{\sqrt {b-c}}}{a}|-\frac {(a-b) b c_1}{(a-c) c c_2}\right )}{(a-c) \sqrt {b (b-c) c_1}}-\frac {\sqrt {2} b \sqrt {a (a-c)} c c_1 \text {sn}\left (\frac {\frac {\sqrt {2} \sqrt {a} \sqrt {a-c} c \sqrt {c_2} t}{\sqrt {b} \sqrt {b-c}}-\frac {\sqrt {2} \sqrt {a} \sqrt {b} \sqrt {a-c} \sqrt {c_2} t}{\sqrt {b-c}}-\frac {\sqrt {2} \sqrt {a} \sqrt {a-c} c \sqrt {c_2} c_3}{\sqrt {b} \sqrt {b-c}}+\frac {\sqrt {2} \sqrt {a} \sqrt {b} \sqrt {a-c} \sqrt {c_2} c_3}{\sqrt {b-c}}}{a}|-\frac {(a-b) b c_1}{(a-c) c c_2}\right )}{(a-c) \sqrt {b (b-c) c_1}}\right ){}^2}{a}-\left (\frac {\sqrt {2} b^2 \sqrt {a (a-c)} c_1 \text {sn}\left (\frac {\frac {\sqrt {2} \sqrt {a} \sqrt {a-c} c \sqrt {c_2} t}{\sqrt {b} \sqrt {b-c}}-\frac {\sqrt {2} \sqrt {a} \sqrt {b} \sqrt {a-c} \sqrt {c_2} t}{\sqrt {b-c}}-\frac {\sqrt {2} \sqrt {a} \sqrt {a-c} c \sqrt {c_2} c_3}{\sqrt {b} \sqrt {b-c}}+\frac {\sqrt {2} \sqrt {a} \sqrt {b} \sqrt {a-c} \sqrt {c_2} c_3}{\sqrt {b-c}}}{a}|-\frac {(a-b) b c_1}{(a-c) c c_2}\right )}{(a-c) \sqrt {b (b-c) c_1}}-\frac {\sqrt {2} b \sqrt {a (a-c)} c c_1 \text {sn}\left (\frac {\frac {\sqrt {2} \sqrt {a} \sqrt {a-c} c \sqrt {c_2} t}{\sqrt {b} \sqrt {b-c}}-\frac {\sqrt {2} \sqrt {a} \sqrt {b} \sqrt {a-c} \sqrt {c_2} t}{\sqrt {b-c}}-\frac {\sqrt {2} \sqrt {a} \sqrt {a-c} c \sqrt {c_2} c_3}{\sqrt {b} \sqrt {b-c}}+\frac {\sqrt {2} \sqrt {a} \sqrt {b} \sqrt {a-c} \sqrt {c_2} c_3}{\sqrt {b-c}}}{a}|-\frac {(a-b) b c_1}{(a-c) c c_2}\right )}{(a-c) \sqrt {b (b-c) c_1}}\right ){}^2}}{\sqrt {b^2-b c}},z(t)\to \frac {\sqrt {-2 c_2 c^2+2 b c_2 c-\frac {b \left (\frac {\sqrt {2} b^2 \sqrt {a (a-c)} c_1 \text {sn}\left (\frac {\frac {\sqrt {2} \sqrt {a} \sqrt {a-c} c \sqrt {c_2} t}{\sqrt {b} \sqrt {b-c}}-\frac {\sqrt {2} \sqrt {a} \sqrt {b} \sqrt {a-c} \sqrt {c_2} t}{\sqrt {b-c}}-\frac {\sqrt {2} \sqrt {a} \sqrt {a-c} c \sqrt {c_2} c_3}{\sqrt {b} \sqrt {b-c}}+\frac {\sqrt {2} \sqrt {a} \sqrt {b} \sqrt {a-c} \sqrt {c_2} c_3}{\sqrt {b-c}}}{a}|-\frac {(a-b) b c_1}{(a-c) c c_2}\right )}{(a-c) \sqrt {b (b-c) c_1}}-\frac {\sqrt {2} b \sqrt {a (a-c)} c c_1 \text {sn}\left (\frac {\frac {\sqrt {2} \sqrt {a} \sqrt {a-c} c \sqrt {c_2} t}{\sqrt {b} \sqrt {b-c}}-\frac {\sqrt {2} \sqrt {a} \sqrt {b} \sqrt {a-c} \sqrt {c_2} t}{\sqrt {b-c}}-\frac {\sqrt {2} \sqrt {a} \sqrt {a-c} c \sqrt {c_2} c_3}{\sqrt {b} \sqrt {b-c}}+\frac {\sqrt {2} \sqrt {a} \sqrt {b} \sqrt {a-c} \sqrt {c_2} c_3}{\sqrt {b-c}}}{a}|-\frac {(a-b) b c_1}{(a-c) c c_2}\right )}{(a-c) \sqrt {b (b-c) c_1}}\right ){}^2}{a}+\left (\frac {\sqrt {2} b^2 \sqrt {a (a-c)} c_1 \text {sn}\left (\frac {\frac {\sqrt {2} \sqrt {a} \sqrt {a-c} c \sqrt {c_2} t}{\sqrt {b} \sqrt {b-c}}-\frac {\sqrt {2} \sqrt {a} \sqrt {b} \sqrt {a-c} \sqrt {c_2} t}{\sqrt {b-c}}-\frac {\sqrt {2} \sqrt {a} \sqrt {a-c} c \sqrt {c_2} c_3}{\sqrt {b} \sqrt {b-c}}+\frac {\sqrt {2} \sqrt {a} \sqrt {b} \sqrt {a-c} \sqrt {c_2} c_3}{\sqrt {b-c}}}{a}|-\frac {(a-b) b c_1}{(a-c) c c_2}\right )}{(a-c) \sqrt {b (b-c) c_1}}-\frac {\sqrt {2} b \sqrt {a (a-c)} c c_1 \text {sn}\left (\frac {\frac {\sqrt {2} \sqrt {a} \sqrt {a-c} c \sqrt {c_2} t}{\sqrt {b} \sqrt {b-c}}-\frac {\sqrt {2} \sqrt {a} \sqrt {b} \sqrt {a-c} \sqrt {c_2} t}{\sqrt {b-c}}-\frac {\sqrt {2} \sqrt {a} \sqrt {a-c} c \sqrt {c_2} c_3}{\sqrt {b} \sqrt {b-c}}+\frac {\sqrt {2} \sqrt {a} \sqrt {b} \sqrt {a-c} \sqrt {c_2} c_3}{\sqrt {b-c}}}{a}|-\frac {(a-b) b c_1}{(a-c) c c_2}\right )}{(a-c) \sqrt {b (b-c) c_1}}\right ){}^2}}{\sqrt {b-c} \sqrt {c}}\right \},\left \{x(t)\to \frac {\frac {\sqrt {2} b^2 \sqrt {a (a-c)} c_1 \text {sn}\left (\frac {\frac {\sqrt {2} \sqrt {a} \sqrt {a-c} c \sqrt {c_2} t}{\sqrt {b} \sqrt {b-c}}-\frac {\sqrt {2} \sqrt {a} \sqrt {b} \sqrt {a-c} \sqrt {c_2} t}{\sqrt {b-c}}-\frac {\sqrt {2} \sqrt {a} \sqrt {a-c} c \sqrt {c_2} c_3}{\sqrt {b} \sqrt {b-c}}+\frac {\sqrt {2} \sqrt {a} \sqrt {b} \sqrt {a-c} \sqrt {c_2} c_3}{\sqrt {b-c}}}{a}|-\frac {(a-b) b c_1}{(a-c) c c_2}\right )}{(a-c) \sqrt {b (b-c) c_1}}-\frac {\sqrt {2} b \sqrt {a (a-c)} c c_1 \text {sn}\left (\frac {\frac {\sqrt {2} \sqrt {a} \sqrt {a-c} c \sqrt {c_2} t}{\sqrt {b} \sqrt {b-c}}-\frac {\sqrt {2} \sqrt {a} \sqrt {b} \sqrt {a-c} \sqrt {c_2} t}{\sqrt {b-c}}-\frac {\sqrt {2} \sqrt {a} \sqrt {a-c} c \sqrt {c_2} c_3}{\sqrt {b} \sqrt {b-c}}+\frac {\sqrt {2} \sqrt {a} \sqrt {b} \sqrt {a-c} \sqrt {c_2} c_3}{\sqrt {b-c}}}{a}|-\frac {(a-b) b c_1}{(a-c) c c_2}\right )}{(a-c) \sqrt {b (b-c) c_1}}}{a},y(t)\to \frac {\sqrt {2 c_1 b^2-2 c c_1 b+\frac {c \left (\frac {\sqrt {2} b^2 \sqrt {a (a-c)} c_1 \text {sn}\left (\frac {\frac {\sqrt {2} \sqrt {a} \sqrt {a-c} c \sqrt {c_2} t}{\sqrt {b} \sqrt {b-c}}-\frac {\sqrt {2} \sqrt {a} \sqrt {b} \sqrt {a-c} \sqrt {c_2} t}{\sqrt {b-c}}-\frac {\sqrt {2} \sqrt {a} \sqrt {a-c} c \sqrt {c_2} c_3}{\sqrt {b} \sqrt {b-c}}+\frac {\sqrt {2} \sqrt {a} \sqrt {b} \sqrt {a-c} \sqrt {c_2} c_3}{\sqrt {b-c}}}{a}|-\frac {(a-b) b c_1}{(a-c) c c_2}\right )}{(a-c) \sqrt {b (b-c) c_1}}-\frac {\sqrt {2} b \sqrt {a (a-c)} c c_1 \text {sn}\left (\frac {\frac {\sqrt {2} \sqrt {a} \sqrt {a-c} c \sqrt {c_2} t}{\sqrt {b} \sqrt {b-c}}-\frac {\sqrt {2} \sqrt {a} \sqrt {b} \sqrt {a-c} \sqrt {c_2} t}{\sqrt {b-c}}-\frac {\sqrt {2} \sqrt {a} \sqrt {a-c} c \sqrt {c_2} c_3}{\sqrt {b} \sqrt {b-c}}+\frac {\sqrt {2} \sqrt {a} \sqrt {b} \sqrt {a-c} \sqrt {c_2} c_3}{\sqrt {b-c}}}{a}|-\frac {(a-b) b c_1}{(a-c) c c_2}\right )}{(a-c) \sqrt {b (b-c) c_1}}\right ){}^2}{a}-\left (\frac {\sqrt {2} b^2 \sqrt {a (a-c)} c_1 \text {sn}\left (\frac {\frac {\sqrt {2} \sqrt {a} \sqrt {a-c} c \sqrt {c_2} t}{\sqrt {b} \sqrt {b-c}}-\frac {\sqrt {2} \sqrt {a} \sqrt {b} \sqrt {a-c} \sqrt {c_2} t}{\sqrt {b-c}}-\frac {\sqrt {2} \sqrt {a} \sqrt {a-c} c \sqrt {c_2} c_3}{\sqrt {b} \sqrt {b-c}}+\frac {\sqrt {2} \sqrt {a} \sqrt {b} \sqrt {a-c} \sqrt {c_2} c_3}{\sqrt {b-c}}}{a}|-\frac {(a-b) b c_1}{(a-c) c c_2}\right )}{(a-c) \sqrt {b (b-c) c_1}}-\frac {\sqrt {2} b \sqrt {a (a-c)} c c_1 \text {sn}\left (\frac {\frac {\sqrt {2} \sqrt {a} \sqrt {a-c} c \sqrt {c_2} t}{\sqrt {b} \sqrt {b-c}}-\frac {\sqrt {2} \sqrt {a} \sqrt {b} \sqrt {a-c} \sqrt {c_2} t}{\sqrt {b-c}}-\frac {\sqrt {2} \sqrt {a} \sqrt {a-c} c \sqrt {c_2} c_3}{\sqrt {b} \sqrt {b-c}}+\frac {\sqrt {2} \sqrt {a} \sqrt {b} \sqrt {a-c} \sqrt {c_2} c_3}{\sqrt {b-c}}}{a}|-\frac {(a-b) b c_1}{(a-c) c c_2}\right )}{(a-c) \sqrt {b (b-c) c_1}}\right ){}^2}}{\sqrt {b^2-b c}},z(t)\to -\frac {\sqrt {-2 c_2 c^2+2 b c_2 c-\frac {b \left (\frac {\sqrt {2} b^2 \sqrt {a (a-c)} c_1 \text {sn}\left (\frac {\frac {\sqrt {2} \sqrt {a} \sqrt {a-c} c \sqrt {c_2} t}{\sqrt {b} \sqrt {b-c}}-\frac {\sqrt {2} \sqrt {a} \sqrt {b} \sqrt {a-c} \sqrt {c_2} t}{\sqrt {b-c}}-\frac {\sqrt {2} \sqrt {a} \sqrt {a-c} c \sqrt {c_2} c_3}{\sqrt {b} \sqrt {b-c}}+\frac {\sqrt {2} \sqrt {a} \sqrt {b} \sqrt {a-c} \sqrt {c_2} c_3}{\sqrt {b-c}}}{a}|-\frac {(a-b) b c_1}{(a-c) c c_2}\right )}{(a-c) \sqrt {b (b-c) c_1}}-\frac {\sqrt {2} b \sqrt {a (a-c)} c c_1 \text {sn}\left (\frac {\frac {\sqrt {2} \sqrt {a} \sqrt {a-c} c \sqrt {c_2} t}{\sqrt {b} \sqrt {b-c}}-\frac {\sqrt {2} \sqrt {a} \sqrt {b} \sqrt {a-c} \sqrt {c_2} t}{\sqrt {b-c}}-\frac {\sqrt {2} \sqrt {a} \sqrt {a-c} c \sqrt {c_2} c_3}{\sqrt {b} \sqrt {b-c}}+\frac {\sqrt {2} \sqrt {a} \sqrt {b} \sqrt {a-c} \sqrt {c_2} c_3}{\sqrt {b-c}}}{a}|-\frac {(a-b) b c_1}{(a-c) c c_2}\right )}{(a-c) \sqrt {b (b-c) c_1}}\right ){}^2}{a}+\left (\frac {\sqrt {2} b^2 \sqrt {a (a-c)} c_1 \text {sn}\left (\frac {\frac {\sqrt {2} \sqrt {a} \sqrt {a-c} c \sqrt {c_2} t}{\sqrt {b} \sqrt {b-c}}-\frac {\sqrt {2} \sqrt {a} \sqrt {b} \sqrt {a-c} \sqrt {c_2} t}{\sqrt {b-c}}-\frac {\sqrt {2} \sqrt {a} \sqrt {a-c} c \sqrt {c_2} c_3}{\sqrt {b} \sqrt {b-c}}+\frac {\sqrt {2} \sqrt {a} \sqrt {b} \sqrt {a-c} \sqrt {c_2} c_3}{\sqrt {b-c}}}{a}|-\frac {(a-b) b c_1}{(a-c) c c_2}\right )}{(a-c) \sqrt {b (b-c) c_1}}-\frac {\sqrt {2} b \sqrt {a (a-c)} c c_1 \text {sn}\left (\frac {\frac {\sqrt {2} \sqrt {a} \sqrt {a-c} c \sqrt {c_2} t}{\sqrt {b} \sqrt {b-c}}-\frac {\sqrt {2} \sqrt {a} \sqrt {b} \sqrt {a-c} \sqrt {c_2} t}{\sqrt {b-c}}-\frac {\sqrt {2} \sqrt {a} \sqrt {a-c} c \sqrt {c_2} c_3}{\sqrt {b} \sqrt {b-c}}+\frac {\sqrt {2} \sqrt {a} \sqrt {b} \sqrt {a-c} \sqrt {c_2} c_3}{\sqrt {b-c}}}{a}|-\frac {(a-b) b c_1}{(a-c) c c_2}\right )}{(a-c) \sqrt {b (b-c) c_1}}\right ){}^2}}{\sqrt {b-c} \sqrt {c}}\right \},\left \{x(t)\to \frac {\frac {\sqrt {2} b^2 \sqrt {a (a-c)} c_1 \text {sn}\left (\frac {-\frac {\sqrt {2} \sqrt {a} \sqrt {a-c} c \sqrt {c_2} t}{\sqrt {b} \sqrt {b-c}}+\frac {\sqrt {2} \sqrt {a} \sqrt {b} \sqrt {a-c} \sqrt {c_2} t}{\sqrt {b-c}}+\frac {\sqrt {2} \sqrt {a} \sqrt {a-c} c \sqrt {c_2} c_3}{\sqrt {b} \sqrt {b-c}}-\frac {\sqrt {2} \sqrt {a} \sqrt {b} \sqrt {a-c} \sqrt {c_2} c_3}{\sqrt {b-c}}}{a}|-\frac {(a-b) b c_1}{(a-c) c c_2}\right )}{(a-c) \sqrt {b (b-c) c_1}}-\frac {\sqrt {2} b \sqrt {a (a-c)} c c_1 \text {sn}\left (\frac {-\frac {\sqrt {2} \sqrt {a} \sqrt {a-c} c \sqrt {c_2} t}{\sqrt {b} \sqrt {b-c}}+\frac {\sqrt {2} \sqrt {a} \sqrt {b} \sqrt {a-c} \sqrt {c_2} t}{\sqrt {b-c}}+\frac {\sqrt {2} \sqrt {a} \sqrt {a-c} c \sqrt {c_2} c_3}{\sqrt {b} \sqrt {b-c}}-\frac {\sqrt {2} \sqrt {a} \sqrt {b} \sqrt {a-c} \sqrt {c_2} c_3}{\sqrt {b-c}}}{a}|-\frac {(a-b) b c_1}{(a-c) c c_2}\right )}{(a-c) \sqrt {b (b-c) c_1}}}{a},y(t)\to -\frac {\sqrt {2 c_1 b^2-2 c c_1 b+\frac {c \left (\frac {\sqrt {2} b^2 \sqrt {a (a-c)} c_1 \text {sn}\left (\frac {-\frac {\sqrt {2} \sqrt {a} \sqrt {a-c} c \sqrt {c_2} t}{\sqrt {b} \sqrt {b-c}}+\frac {\sqrt {2} \sqrt {a} \sqrt {b} \sqrt {a-c} \sqrt {c_2} t}{\sqrt {b-c}}+\frac {\sqrt {2} \sqrt {a} \sqrt {a-c} c \sqrt {c_2} c_3}{\sqrt {b} \sqrt {b-c}}-\frac {\sqrt {2} \sqrt {a} \sqrt {b} \sqrt {a-c} \sqrt {c_2} c_3}{\sqrt {b-c}}}{a}|-\frac {(a-b) b c_1}{(a-c) c c_2}\right )}{(a-c) \sqrt {b (b-c) c_1}}-\frac {\sqrt {2} b \sqrt {a (a-c)} c c_1 \text {sn}\left (\frac {-\frac {\sqrt {2} \sqrt {a} \sqrt {a-c} c \sqrt {c_2} t}{\sqrt {b} \sqrt {b-c}}+\frac {\sqrt {2} \sqrt {a} \sqrt {b} \sqrt {a-c} \sqrt {c_2} t}{\sqrt {b-c}}+\frac {\sqrt {2} \sqrt {a} \sqrt {a-c} c \sqrt {c_2} c_3}{\sqrt {b} \sqrt {b-c}}-\frac {\sqrt {2} \sqrt {a} \sqrt {b} \sqrt {a-c} \sqrt {c_2} c_3}{\sqrt {b-c}}}{a}|-\frac {(a-b) b c_1}{(a-c) c c_2}\right )}{(a-c) \sqrt {b (b-c) c_1}}\right ){}^2}{a}-\left (\frac {\sqrt {2} b^2 \sqrt {a (a-c)} c_1 \text {sn}\left (\frac {-\frac {\sqrt {2} \sqrt {a} \sqrt {a-c} c \sqrt {c_2} t}{\sqrt {b} \sqrt {b-c}}+\frac {\sqrt {2} \sqrt {a} \sqrt {b} \sqrt {a-c} \sqrt {c_2} t}{\sqrt {b-c}}+\frac {\sqrt {2} \sqrt {a} \sqrt {a-c} c \sqrt {c_2} c_3}{\sqrt {b} \sqrt {b-c}}-\frac {\sqrt {2} \sqrt {a} \sqrt {b} \sqrt {a-c} \sqrt {c_2} c_3}{\sqrt {b-c}}}{a}|-\frac {(a-b) b c_1}{(a-c) c c_2}\right )}{(a-c) \sqrt {b (b-c) c_1}}-\frac {\sqrt {2} b \sqrt {a (a-c)} c c_1 \text {sn}\left (\frac {-\frac {\sqrt {2} \sqrt {a} \sqrt {a-c} c \sqrt {c_2} t}{\sqrt {b} \sqrt {b-c}}+\frac {\sqrt {2} \sqrt {a} \sqrt {b} \sqrt {a-c} \sqrt {c_2} t}{\sqrt {b-c}}+\frac {\sqrt {2} \sqrt {a} \sqrt {a-c} c \sqrt {c_2} c_3}{\sqrt {b} \sqrt {b-c}}-\frac {\sqrt {2} \sqrt {a} \sqrt {b} \sqrt {a-c} \sqrt {c_2} c_3}{\sqrt {b-c}}}{a}|-\frac {(a-b) b c_1}{(a-c) c c_2}\right )}{(a-c) \sqrt {b (b-c) c_1}}\right ){}^2}}{\sqrt {b^2-b c}},z(t)\to -\frac {\sqrt {-2 c_2 c^2+2 b c_2 c-\frac {b \left (\frac {\sqrt {2} b^2 \sqrt {a (a-c)} c_1 \text {sn}\left (\frac {-\frac {\sqrt {2} \sqrt {a} \sqrt {a-c} c \sqrt {c_2} t}{\sqrt {b} \sqrt {b-c}}+\frac {\sqrt {2} \sqrt {a} \sqrt {b} \sqrt {a-c} \sqrt {c_2} t}{\sqrt {b-c}}+\frac {\sqrt {2} \sqrt {a} \sqrt {a-c} c \sqrt {c_2} c_3}{\sqrt {b} \sqrt {b-c}}-\frac {\sqrt {2} \sqrt {a} \sqrt {b} \sqrt {a-c} \sqrt {c_2} c_3}{\sqrt {b-c}}}{a}|-\frac {(a-b) b c_1}{(a-c) c c_2}\right )}{(a-c) \sqrt {b (b-c) c_1}}-\frac {\sqrt {2} b \sqrt {a (a-c)} c c_1 \text {sn}\left (\frac {-\frac {\sqrt {2} \sqrt {a} \sqrt {a-c} c \sqrt {c_2} t}{\sqrt {b} \sqrt {b-c}}+\frac {\sqrt {2} \sqrt {a} \sqrt {b} \sqrt {a-c} \sqrt {c_2} t}{\sqrt {b-c}}+\frac {\sqrt {2} \sqrt {a} \sqrt {a-c} c \sqrt {c_2} c_3}{\sqrt {b} \sqrt {b-c}}-\frac {\sqrt {2} \sqrt {a} \sqrt {b} \sqrt {a-c} \sqrt {c_2} c_3}{\sqrt {b-c}}}{a}|-\frac {(a-b) b c_1}{(a-c) c c_2}\right )}{(a-c) \sqrt {b (b-c) c_1}}\right ){}^2}{a}+\left (\frac {\sqrt {2} b^2 \sqrt {a (a-c)} c_1 \text {sn}\left (\frac {-\frac {\sqrt {2} \sqrt {a} \sqrt {a-c} c \sqrt {c_2} t}{\sqrt {b} \sqrt {b-c}}+\frac {\sqrt {2} \sqrt {a} \sqrt {b} \sqrt {a-c} \sqrt {c_2} t}{\sqrt {b-c}}+\frac {\sqrt {2} \sqrt {a} \sqrt {a-c} c \sqrt {c_2} c_3}{\sqrt {b} \sqrt {b-c}}-\frac {\sqrt {2} \sqrt {a} \sqrt {b} \sqrt {a-c} \sqrt {c_2} c_3}{\sqrt {b-c}}}{a}|-\frac {(a-b) b c_1}{(a-c) c c_2}\right )}{(a-c) \sqrt {b (b-c) c_1}}-\frac {\sqrt {2} b \sqrt {a (a-c)} c c_1 \text {sn}\left (\frac {-\frac {\sqrt {2} \sqrt {a} \sqrt {a-c} c \sqrt {c_2} t}{\sqrt {b} \sqrt {b-c}}+\frac {\sqrt {2} \sqrt {a} \sqrt {b} \sqrt {a-c} \sqrt {c_2} t}{\sqrt {b-c}}+\frac {\sqrt {2} \sqrt {a} \sqrt {a-c} c \sqrt {c_2} c_3}{\sqrt {b} \sqrt {b-c}}-\frac {\sqrt {2} \sqrt {a} \sqrt {b} \sqrt {a-c} \sqrt {c_2} c_3}{\sqrt {b-c}}}{a}|-\frac {(a-b) b c_1}{(a-c) c c_2}\right )}{(a-c) \sqrt {b (b-c) c_1}}\right ){}^2}}{\sqrt {b-c} \sqrt {c}}\right \},\left \{x(t)\to \frac {\frac {\sqrt {2} b^2 \sqrt {a (a-c)} c_1 \text {sn}\left (\frac {-\frac {\sqrt {2} \sqrt {a} \sqrt {a-c} c \sqrt {c_2} t}{\sqrt {b} \sqrt {b-c}}+\frac {\sqrt {2} \sqrt {a} \sqrt {b} \sqrt {a-c} \sqrt {c_2} t}{\sqrt {b-c}}+\frac {\sqrt {2} \sqrt {a} \sqrt {a-c} c \sqrt {c_2} c_3}{\sqrt {b} \sqrt {b-c}}-\frac {\sqrt {2} \sqrt {a} \sqrt {b} \sqrt {a-c} \sqrt {c_2} c_3}{\sqrt {b-c}}}{a}|-\frac {(a-b) b c_1}{(a-c) c c_2}\right )}{(a-c) \sqrt {b (b-c) c_1}}-\frac {\sqrt {2} b \sqrt {a (a-c)} c c_1 \text {sn}\left (\frac {-\frac {\sqrt {2} \sqrt {a} \sqrt {a-c} c \sqrt {c_2} t}{\sqrt {b} \sqrt {b-c}}+\frac {\sqrt {2} \sqrt {a} \sqrt {b} \sqrt {a-c} \sqrt {c_2} t}{\sqrt {b-c}}+\frac {\sqrt {2} \sqrt {a} \sqrt {a-c} c \sqrt {c_2} c_3}{\sqrt {b} \sqrt {b-c}}-\frac {\sqrt {2} \sqrt {a} \sqrt {b} \sqrt {a-c} \sqrt {c_2} c_3}{\sqrt {b-c}}}{a}|-\frac {(a-b) b c_1}{(a-c) c c_2}\right )}{(a-c) \sqrt {b (b-c) c_1}}}{a},y(t)\to \frac {\sqrt {2 c_1 b^2-2 c c_1 b+\frac {c \left (\frac {\sqrt {2} b^2 \sqrt {a (a-c)} c_1 \text {sn}\left (\frac {-\frac {\sqrt {2} \sqrt {a} \sqrt {a-c} c \sqrt {c_2} t}{\sqrt {b} \sqrt {b-c}}+\frac {\sqrt {2} \sqrt {a} \sqrt {b} \sqrt {a-c} \sqrt {c_2} t}{\sqrt {b-c}}+\frac {\sqrt {2} \sqrt {a} \sqrt {a-c} c \sqrt {c_2} c_3}{\sqrt {b} \sqrt {b-c}}-\frac {\sqrt {2} \sqrt {a} \sqrt {b} \sqrt {a-c} \sqrt {c_2} c_3}{\sqrt {b-c}}}{a}|-\frac {(a-b) b c_1}{(a-c) c c_2}\right )}{(a-c) \sqrt {b (b-c) c_1}}-\frac {\sqrt {2} b \sqrt {a (a-c)} c c_1 \text {sn}\left (\frac {-\frac {\sqrt {2} \sqrt {a} \sqrt {a-c} c \sqrt {c_2} t}{\sqrt {b} \sqrt {b-c}}+\frac {\sqrt {2} \sqrt {a} \sqrt {b} \sqrt {a-c} \sqrt {c_2} t}{\sqrt {b-c}}+\frac {\sqrt {2} \sqrt {a} \sqrt {a-c} c \sqrt {c_2} c_3}{\sqrt {b} \sqrt {b-c}}-\frac {\sqrt {2} \sqrt {a} \sqrt {b} \sqrt {a-c} \sqrt {c_2} c_3}{\sqrt {b-c}}}{a}|-\frac {(a-b) b c_1}{(a-c) c c_2}\right )}{(a-c) \sqrt {b (b-c) c_1}}\right ){}^2}{a}-\left (\frac {\sqrt {2} b^2 \sqrt {a (a-c)} c_1 \text {sn}\left (\frac {-\frac {\sqrt {2} \sqrt {a} \sqrt {a-c} c \sqrt {c_2} t}{\sqrt {b} \sqrt {b-c}}+\frac {\sqrt {2} \sqrt {a} \sqrt {b} \sqrt {a-c} \sqrt {c_2} t}{\sqrt {b-c}}+\frac {\sqrt {2} \sqrt {a} \sqrt {a-c} c \sqrt {c_2} c_3}{\sqrt {b} \sqrt {b-c}}-\frac {\sqrt {2} \sqrt {a} \sqrt {b} \sqrt {a-c} \sqrt {c_2} c_3}{\sqrt {b-c}}}{a}|-\frac {(a-b) b c_1}{(a-c) c c_2}\right )}{(a-c) \sqrt {b (b-c) c_1}}-\frac {\sqrt {2} b \sqrt {a (a-c)} c c_1 \text {sn}\left (\frac {-\frac {\sqrt {2} \sqrt {a} \sqrt {a-c} c \sqrt {c_2} t}{\sqrt {b} \sqrt {b-c}}+\frac {\sqrt {2} \sqrt {a} \sqrt {b} \sqrt {a-c} \sqrt {c_2} t}{\sqrt {b-c}}+\frac {\sqrt {2} \sqrt {a} \sqrt {a-c} c \sqrt {c_2} c_3}{\sqrt {b} \sqrt {b-c}}-\frac {\sqrt {2} \sqrt {a} \sqrt {b} \sqrt {a-c} \sqrt {c_2} c_3}{\sqrt {b-c}}}{a}|-\frac {(a-b) b c_1}{(a-c) c c_2}\right )}{(a-c) \sqrt {b (b-c) c_1}}\right ){}^2}}{\sqrt {b^2-b c}},z(t)\to \frac {\sqrt {-2 c_2 c^2+2 b c_2 c-\frac {b \left (\frac {\sqrt {2} b^2 \sqrt {a (a-c)} c_1 \text {sn}\left (\frac {-\frac {\sqrt {2} \sqrt {a} \sqrt {a-c} c \sqrt {c_2} t}{\sqrt {b} \sqrt {b-c}}+\frac {\sqrt {2} \sqrt {a} \sqrt {b} \sqrt {a-c} \sqrt {c_2} t}{\sqrt {b-c}}+\frac {\sqrt {2} \sqrt {a} \sqrt {a-c} c \sqrt {c_2} c_3}{\sqrt {b} \sqrt {b-c}}-\frac {\sqrt {2} \sqrt {a} \sqrt {b} \sqrt {a-c} \sqrt {c_2} c_3}{\sqrt {b-c}}}{a}|-\frac {(a-b) b c_1}{(a-c) c c_2}\right )}{(a-c) \sqrt {b (b-c) c_1}}-\frac {\sqrt {2} b \sqrt {a (a-c)} c c_1 \text {sn}\left (\frac {-\frac {\sqrt {2} \sqrt {a} \sqrt {a-c} c \sqrt {c_2} t}{\sqrt {b} \sqrt {b-c}}+\frac {\sqrt {2} \sqrt {a} \sqrt {b} \sqrt {a-c} \sqrt {c_2} t}{\sqrt {b-c}}+\frac {\sqrt {2} \sqrt {a} \sqrt {a-c} c \sqrt {c_2} c_3}{\sqrt {b} \sqrt {b-c}}-\frac {\sqrt {2} \sqrt {a} \sqrt {b} \sqrt {a-c} \sqrt {c_2} c_3}{\sqrt {b-c}}}{a}|-\frac {(a-b) b c_1}{(a-c) c c_2}\right )}{(a-c) \sqrt {b (b-c) c_1}}\right ){}^2}{a}+\left (\frac {\sqrt {2} b^2 \sqrt {a (a-c)} c_1 \text {sn}\left (\frac {-\frac {\sqrt {2} \sqrt {a} \sqrt {a-c} c \sqrt {c_2} t}{\sqrt {b} \sqrt {b-c}}+\frac {\sqrt {2} \sqrt {a} \sqrt {b} \sqrt {a-c} \sqrt {c_2} t}{\sqrt {b-c}}+\frac {\sqrt {2} \sqrt {a} \sqrt {a-c} c \sqrt {c_2} c_3}{\sqrt {b} \sqrt {b-c}}-\frac {\sqrt {2} \sqrt {a} \sqrt {b} \sqrt {a-c} \sqrt {c_2} c_3}{\sqrt {b-c}}}{a}|-\frac {(a-b) b c_1}{(a-c) c c_2}\right )}{(a-c) \sqrt {b (b-c) c_1}}-\frac {\sqrt {2} b \sqrt {a (a-c)} c c_1 \text {sn}\left (\frac {-\frac {\sqrt {2} \sqrt {a} \sqrt {a-c} c \sqrt {c_2} t}{\sqrt {b} \sqrt {b-c}}+\frac {\sqrt {2} \sqrt {a} \sqrt {b} \sqrt {a-c} \sqrt {c_2} t}{\sqrt {b-c}}+\frac {\sqrt {2} \sqrt {a} \sqrt {a-c} c \sqrt {c_2} c_3}{\sqrt {b} \sqrt {b-c}}-\frac {\sqrt {2} \sqrt {a} \sqrt {b} \sqrt {a-c} \sqrt {c_2} c_3}{\sqrt {b-c}}}{a}|-\frac {(a-b) b c_1}{(a-c) c c_2}\right )}{(a-c) \sqrt {b (b-c) c_1}}\right ){}^2}}{\sqrt {b-c} \sqrt {c}}\right \}\right \} \]
Maple: cpu = 0.514 (sec), leaf count = 1356 \[ \left \{ [ \left \{ x \left ( t \right ) =0 \right \} , \left \{ y \left ( t \right ) =0 \right \} , \left \{ z \left ( t \right ) ={\it \_C1} \right \} ],[ \left \{ x \left ( t \right ) =0 \right \} , \left \{ y \left ( t \right ) ={\it \_C1} \right \} , \left \{ z \left ( t \right ) =0 \right \} ],[ \left \{ x \left ( t \right ) ={\it \_C1} \right \} , \left \{ y \left ( t \right ) =0 \right \} , \left \{ z \left ( t \right ) =0 \right \} ],[ \left \{ x \left ( t \right ) ={\it RootOf} \left ( -\int ^{ {\it \_Z}}\!-2\,{\frac {bc \left ( {a}^{2}-ab-ac+bc \right ) }{\sqrt {bc \left ( {a}^{2}-ab-ac+bc \right ) \left ( -4\,{{\it \_a}}^{4}{a}^{4}+8 \,{{\it \_a}}^{4}{a}^{3}b+8\,{{\it \_a}}^{4}{a}^{3}c-4\,{{\it \_a}}^{4 }{a}^{2}{b}^{2}-16\,{{\it \_a}}^{4}{a}^{2}bc-4\,{{\it \_a}}^{4}{a}^{2} {c}^{2}+8\,{{\it \_a}}^{4}a{b}^{2}c+8\,{{\it \_a}}^{4}ab{c}^{2}-4\,{{ \it \_a}}^{4}{b}^{2}{c}^{2}+16\,{\it \_C2}\,{{\it \_a}}^{2}{a}^{4}-32 \,{\it \_C2}\,{{\it \_a}}^{2}{a}^{3}b-32\,{\it \_C2}\,{{\it \_a}}^{2}{ a}^{3}c+16\,{\it \_C2}\,{{\it \_a}}^{2}{a}^{2}{b}^{2}+64\,{\it \_C2}\, {{\it \_a}}^{2}{a}^{2}bc+16\,{\it \_C2}\,{{\it \_a}}^{2}{a}^{2}{c}^{2} -32\,{\it \_C2}\,{{\it \_a}}^{2}a{b}^{2}c-32\,{\it \_C2}\,{{\it \_a}}^ {2}ab{c}^{2}+16\,{\it \_C2}\,{{\it \_a}}^{2}{b}^{2}{c}^{2}-16\,{{\it \_C2}}^{2}{a}^{4}+32\,{{\it \_C2}}^{2}{a}^{3}b+32\,{{\it \_C2}}^{2}{a} ^{3}c-16\,{{\it \_C2}}^{2}{a}^{2}{b}^{2}-64\,{{\it \_C2}}^{2}{a}^{2}bc -16\,{{\it \_C2}}^{2}{a}^{2}{c}^{2}+32\,{{\it \_C2}}^{2}a{b}^{2}c+32\, {{\it \_C2}}^{2}ab{c}^{2}-16\,{{\it \_C2}}^{2}{b}^{2}{c}^{2}+{\it \_C1 }\,bc \right ) }}}{d{\it \_a}}+t+{\it \_C3} \right ) ,x \left ( t \right ) ={\it RootOf} \left ( -\int ^{{\it \_Z}}\!2\,{\frac {bc \left ( {a}^{2}-ab-ac+bc \right ) }{\sqrt {bc \left ( {a}^{2}-ab-ac+bc \right ) \left ( -4\,{{\it \_a}}^{4}{a}^{4}+8\,{{\it \_a}}^{4}{a}^{3}b +8\,{{\it \_a}}^{4}{a}^{3}c-4\,{{\it \_a}}^{4}{a}^{2}{b}^{2}-16\,{{ \it \_a}}^{4}{a}^{2}bc-4\,{{\it \_a}}^{4}{a}^{2}{c}^{2}+8\,{{\it \_a}} ^{4}a{b}^{2}c+8\,{{\it \_a}}^{4}ab{c}^{2}-4\,{{\it \_a}}^{4}{b}^{2}{c} ^{2}+16\,{\it \_C2}\,{{\it \_a}}^{2}{a}^{4}-32\,{\it \_C2}\,{{\it \_a} }^{2}{a}^{3}b-32\,{\it \_C2}\,{{\it \_a}}^{2}{a}^{3}c+16\,{\it \_C2}\, {{\it \_a}}^{2}{a}^{2}{b}^{2}+64\,{\it \_C2}\,{{\it \_a}}^{2}{a}^{2}bc +16\,{\it \_C2}\,{{\it \_a}}^{2}{a}^{2}{c}^{2}-32\,{\it \_C2}\,{{\it \_a}}^{2}a{b}^{2}c-32\,{\it \_C2}\,{{\it \_a}}^{2}ab{c}^{2}+16\,{\it \_C2}\,{{\it \_a}}^{2}{b}^{2}{c}^{2}-16\,{{\it \_C2}}^{2}{a}^{4}+32\,{ {\it \_C2}}^{2}{a}^{3}b+32\,{{\it \_C2}}^{2}{a}^{3}c-16\,{{\it \_C2}}^ {2}{a}^{2}{b}^{2}-64\,{{\it \_C2}}^{2}{a}^{2}bc-16\,{{\it \_C2}}^{2}{a }^{2}{c}^{2}+32\,{{\it \_C2}}^{2}a{b}^{2}c+32\,{{\it \_C2}}^{2}ab{c}^{ 2}-16\,{{\it \_C2}}^{2}{b}^{2}{c}^{2}+{\it \_C1}\,bc \right ) }}}{d{ \it \_a}}+t+{\it \_C3} \right ) \right \} , \left \{ y \left ( t \right ) =-{\frac {\sqrt {2}}{2\,bx \left ( t \right ) \left ( ab-ac-{b}^{2}+bc \right ) }\sqrt {x \left ( t \right ) b \left ( ab-ac-{b}^{2}+bc \right ) \left ( \left ( {\frac {{\rm d}^{2}}{{\rm d}{t}^{2}}}x \left ( t \right ) \right ) cb-\sqrt {4\, \left ( x \left ( t \right ) \right ) ^{2 } \left ( {\frac {\rm d}{{\rm d}t}}x \left ( t \right ) \right ) ^{2}{a}^ {2}bc-4\, \left ( x \left ( t \right ) \right ) ^{2} \left ( {\frac {\rm d}{{\rm d}t}}x \left ( t \right ) \right ) ^{2}a{b}^{2}c-4\, \left ( x \left ( t \right ) \right ) ^{2} \left ( {\frac {\rm d}{{\rm d} t}}x \left ( t \right ) \right ) ^{2}ab{c}^{2}+4\, \left ( x \left ( t \right ) \right ) ^{2} \left ( {\frac {\rm d}{{\rm d}t}}x \left ( t \right ) \right ) ^{2}{b}^{2}{c}^{2}+ \left ( {\frac {{\rm d}^{2}}{ {\rm d}{t}^{2}}}x \left ( t \right ) \right ) ^{2}{b}^{2}{c}^{2}} \right ) a}},y \left ( t \right ) ={\frac {\sqrt {2}}{2\,bx \left ( t \right ) \left ( ab-ac-{b}^{2}+bc \right ) }\sqrt {x \left ( t \right ) b \left ( ab-ac-{b}^{2}+bc \right ) \left ( \left ( {\frac {{\rm d}^{2}}{ {\rm d}{t}^{2}}}x \left ( t \right ) \right ) cb-\sqrt {4\, \left ( x \left ( t \right ) \right ) ^{2} \left ( {\frac {\rm d}{{\rm d}t}}x \left ( t \right ) \right ) ^{2}{a}^{2}bc-4\, \left ( x \left ( t \right ) \right ) ^{2} \left ( {\frac {\rm d}{{\rm d}t}}x \left ( t \right ) \right ) ^{2}a{b}^{2}c-4\, \left ( x \left ( t \right ) \right ) ^{2} \left ( {\frac {\rm d}{{\rm d}t}}x \left ( t \right ) \right ) ^{2}ab{c}^{2}+4\, \left ( x \left ( t \right ) \right ) ^{2} \left ( {\frac {\rm d}{{\rm d}t}}x \left ( t \right ) \right ) ^{2}{b}^{ 2}{c}^{2}+ \left ( {\frac {{\rm d}^{2}}{{\rm d}{t}^{2}}}x \left ( t \right ) \right ) ^{2}{b}^{2}{c}^{2}} \right ) a}},y \left ( t \right ) = -{\frac {\sqrt {2}}{2\,bx \left ( t \right ) \left ( ab-ac-{b}^{2}+bc \right ) }\sqrt {x \left ( t \right ) b \left ( ab-ac-{b}^{2}+bc \right ) \left ( \left ( {\frac {{\rm d}^{2}}{{\rm d}{t}^{2}}}x \left ( t \right ) \right ) cb+\sqrt {4\, \left ( x \left ( t \right ) \right ) ^{2 } \left ( {\frac {\rm d}{{\rm d}t}}x \left ( t \right ) \right ) ^{2}{a}^ {2}bc-4\, \left ( x \left ( t \right ) \right ) ^{2} \left ( {\frac {\rm d}{{\rm d}t}}x \left ( t \right ) \right ) ^{2}a{b}^{2}c-4\, \left ( x \left ( t \right ) \right ) ^{2} \left ( {\frac {\rm d}{{\rm d} t}}x \left ( t \right ) \right ) ^{2}ab{c}^{2}+4\, \left ( x \left ( t \right ) \right ) ^{2} \left ( {\frac {\rm d}{{\rm d}t}}x \left ( t \right ) \right ) ^{2}{b}^{2}{c}^{2}+ \left ( {\frac {{\rm d}^{2}}{ {\rm d}{t}^{2}}}x \left ( t \right ) \right ) ^{2}{b}^{2}{c}^{2}} \right ) a}},y \left ( t \right ) ={\frac {\sqrt {2}}{2\,bx \left ( t \right ) \left ( ab-ac-{b}^{2}+bc \right ) }\sqrt {x \left ( t \right ) b \left ( ab-ac-{b}^{2}+bc \right ) \left ( \left ( {\frac {{\rm d}^{2}}{ {\rm d}{t}^{2}}}x \left ( t \right ) \right ) cb+\sqrt {4\, \left ( x \left ( t \right ) \right ) ^{2} \left ( {\frac {\rm d}{{\rm d}t}}x \left ( t \right ) \right ) ^{2}{a}^{2}bc-4\, \left ( x \left ( t \right ) \right ) ^{2} \left ( {\frac {\rm d}{{\rm d}t}}x \left ( t \right ) \right ) ^{2}a{b}^{2}c-4\, \left ( x \left ( t \right ) \right ) ^{2} \left ( {\frac {\rm d}{{\rm d}t}}x \left ( t \right ) \right ) ^{2}ab{c}^{2}+4\, \left ( x \left ( t \right ) \right ) ^{2} \left ( {\frac {\rm d}{{\rm d}t}}x \left ( t \right ) \right ) ^{2}{b}^{ 2}{c}^{2}+ \left ( {\frac {{\rm d}^{2}}{{\rm d}{t}^{2}}}x \left ( t \right ) \right ) ^{2}{b}^{2}{c}^{2}} \right ) a}} \right \} , \left \{ z \left ( t \right ) ={\frac {a{\frac {\rm d}{{\rm d}t}}x \left ( t \right ) }{by \left ( t \right ) -cy \left ( t \right ) }} \right \} ] \right \} \]