\[ \left \{a x'(t)=(b-c) y(t) z(t),b y'(t)=(c-a) x(t) z(t),c z'(t)=(a-b) x(t) y(t)\right \} \] ✓ Mathematica : cpu = 5.57203 (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 = 0.632 (sec), leaf count = 695
\[ \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}}\! \left ( {\it RootOf} \left ( -{{\it \_a}}^{2}-2\,\int ^{{\it \_Z}}\!{\frac {\sqrt {-{\it \_C1}\,cb \left ( 4\,{\it \_C1}\,{{\it \_h}}^{2}{a}^{2}-4\,{\it \_C1}\,{{\it \_h}}^{2}ab-4\,{\it \_C1}\,{{\it \_h}}^{2}ac+4\,{\it \_C1}\,{{\it \_h}}^{2}bc-1 \right ) }{\it \_h}}{4\,{\it \_C1}\,{{\it \_h}}^{2}{a}^{2}-4\,{\it \_C1}\,{{\it \_h}}^{2}ab-4\,{\it \_C1}\,{{\it \_h}}^{2}ac+4\,{\it \_C1}\,{{\it \_h}}^{2}bc-1}}{d{\it \_h}}+2\,{\it \_C2} \right ) \right ) ^{-1}{d{\it \_a}}+t+{\it \_C3} \right ) ,x \left ( t \right ) ={\it RootOf} \left ( -\int ^{{\it \_Z}}\! \left ( {\it RootOf} \left ( -{{\it \_a}}^{2}+2\,\int ^{{\it \_Z}}\!{\frac {\sqrt {-{\it \_C1}\,cb \left ( 4\,{\it \_C1}\,{{\it \_h}}^{2}{a}^{2}-4\,{\it \_C1}\,{{\it \_h}}^{2}ab-4\,{\it \_C1}\,{{\it \_h}}^{2}ac+4\,{\it \_C1}\,{{\it \_h}}^{2}bc-1 \right ) }{\it \_h}}{4\,{\it \_C1}\,{{\it \_h}}^{2}{a}^{2}-4\,{\it \_C1}\,{{\it \_h}}^{2}ab-4\,{\it \_C1}\,{{\it \_h}}^{2}ac+4\,{\it \_C1}\,{{\it \_h}}^{2}bc-1}}{d{\it \_h}}+2\,{\it \_C2} \right ) \right ) ^{-1}{d{\it \_a}}+t+{\it \_C3} \right ) \right \} , \left \{ y \left ( t \right ) =-{\frac {\sqrt {2}}{2\,bx \left ( t \right ) \left ( b-c \right ) \left ( a-b \right ) }\sqrt {x \left ( t \right ) b \left ( b-c \right ) \left ( a-b \right ) \left ( \left ( {\frac {{\rm d}^{2}}{{\rm d}{t}^{2}}}x \left ( t \right ) \right ) bc-\sqrt {4}\sqrt { \left ( {\frac {bc \left ( {\frac {{\rm d}^{2}}{{\rm d}{t}^{2}}}x \left ( t \right ) \right ) ^{2}}{4}}+ \left ( x \left ( t \right ) \right ) ^{2} \left ( {\frac {\rm d}{{\rm d}t}}x \left ( t \right ) \right ) ^{2} \left ( a-c \right ) \left ( a-b \right ) \right ) cb} \right ) a}},y \left ( t \right ) ={\frac {\sqrt {2}}{2\,bx \left ( t \right ) \left ( b-c \right ) \left ( a-b \right ) }\sqrt {x \left ( t \right ) b \left ( b-c \right ) \left ( a-b \right ) \left ( \left ( {\frac {{\rm d}^{2}}{{\rm d}{t}^{2}}}x \left ( t \right ) \right ) bc-\sqrt {4}\sqrt { \left ( {\frac {bc \left ( {\frac {{\rm d}^{2}}{{\rm d}{t}^{2}}}x \left ( t \right ) \right ) ^{2}}{4}}+ \left ( x \left ( t \right ) \right ) ^{2} \left ( {\frac {\rm d}{{\rm d}t}}x \left ( t \right ) \right ) ^{2} \left ( a-c \right ) \left ( a-b \right ) \right ) cb} \right ) a}},y \left ( t \right ) =-{\frac {\sqrt {2}}{2\,bx \left ( t \right ) \left ( b-c \right ) \left ( a-b \right ) }\sqrt {x \left ( t \right ) b \left ( b-c \right ) \left ( a-b \right ) \left ( \left ( {\frac {{\rm d}^{2}}{{\rm d}{t}^{2}}}x \left ( t \right ) \right ) bc+\sqrt {4}\sqrt { \left ( {\frac {bc \left ( {\frac {{\rm d}^{2}}{{\rm d}{t}^{2}}}x \left ( t \right ) \right ) ^{2}}{4}}+ \left ( x \left ( t \right ) \right ) ^{2} \left ( {\frac {\rm d}{{\rm d}t}}x \left ( t \right ) \right ) ^{2} \left ( a-c \right ) \left ( a-b \right ) \right ) cb} \right ) a}},y \left ( t \right ) ={\frac {\sqrt {2}}{2\,bx \left ( t \right ) \left ( b-c \right ) \left ( a-b \right ) }\sqrt {x \left ( t \right ) b \left ( b-c \right ) \left ( a-b \right ) \left ( \left ( {\frac {{\rm d}^{2}}{{\rm d}{t}^{2}}}x \left ( t \right ) \right ) bc+\sqrt {4}\sqrt { \left ( {\frac {bc \left ( {\frac {{\rm d}^{2}}{{\rm d}{t}^{2}}}x \left ( t \right ) \right ) ^{2}}{4}}+ \left ( x \left ( t \right ) \right ) ^{2} \left ( {\frac {\rm d}{{\rm d}t}}x \left ( t \right ) \right ) ^{2} \left ( a-c \right ) \left ( a-b \right ) \right ) cb} \right ) a}} \right \} , \left \{ z \left ( t \right ) ={\frac {a{\frac {\rm d}{{\rm d}t}}x \left ( t \right ) }{y \left ( t \right ) \left ( b-c \right ) }} \right \} ] \right \} \]