2.1931   ODE No. 1931

\[ \left \{a x'(t)=(b-c) y(t) z(t),b y'(t)=(c-a) x(t) z(t),c z'(t)=(a-b) x(t) y(t)\right \} \] Mathematica : cpu = 3.70285 (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 = 1.096 (sec), leaf count = 1117


\[[\{x \relax (t ) = 0\}, \{y \relax (t ) = 0\}, \{z \relax (t ) = c_{1}\}]\]