\[ \left \{x'(t)=-x(t) y(t)^2+x(t)+y(t),y'(t)=x(t)^2 y(t)-x(t)-y(t),z'(t)=y(t)^2-x(t)^2\right \} \] ✗ Mathematica : cpu = 0.757668 (sec), leaf count = 0 , could not solve
DSolve[{Derivative[1][x][t] == x[t] + y[t] - x[t]*y[t]^2, Derivative[1][y][t] == -x[t] - y[t] + x[t]^2*y[t], Derivative[1][z][t] == -x[t]^2 + y[t]^2}, {x[t], y[t], z[t]}, t]
✓ Maple : cpu = 1.039 (sec), leaf count = 242
\[\left \{[\{x \left (t \right ) = 0\}, \{y \left (t \right ) = 0\}, \{z \left (t \right ) = c_{1}\}], \left [\left \{x \left (t \right ) = \mathit {ODESolStruc} \left (\textit {\_a} , \left [\left \{\frac {4 \textit {\_a}^{5}+2 \textit {\_a}^{2} \textit {\_}b\left (\textit {\_a} \right ) \left (\frac {d}{d \textit {\_a}}\mathrm {\_}\mathrm {b}\left (\textit {\_a} \right )\right )-3 \textit {\_a}^{3}-2 \textit {\_a} \textit {\_}b\left (\textit {\_a} \right )^{2}-\textit {\_a} +\left (-4 \textit {\_a}^{4}+4 \textit {\_a}^{2}+1\right ) \textit {\_}b\left (\textit {\_a} \right )+\sqrt {\left (4 \textit {\_a}^{2}-4 \textit {\_a} \textit {\_}b\left (\textit {\_a} \right )+1\right ) \left (\textit {\_a}^{3}+\textit {\_a} -\textit {\_}b\left (\textit {\_a} \right )\right )^{2}}}{2 \textit {\_a}^{2}}=0\right \}, \left \{\textit {\_a} =x \left (t \right ), \textit {\_}b\left (\textit {\_a} \right )=\frac {d}{d t}x \left (t \right )\right \}, \left \{t =c_{2}+\int \frac {1}{\textit {\_}b\left (\textit {\_a} \right )}d \textit {\_a} , x \left (t \right )=\textit {\_a} \right \}\right ]\right )\right \}, \left \{y \left (t \right ) = \frac {\left (\frac {d^{2}}{d t^{2}}x \left (t \right )\right ) x \left (t \right )+2 \left (x \left (t \right )^{3}+\frac {\frac {d}{d t}x \left (t \right )}{2}-\frac {x \left (t \right )}{2}\right ) \left (-\frac {d}{d t}x \left (t \right )+x \left (t \right )\right )}{x \left (t \right )^{3}-\frac {d}{d t}x \left (t \right )+x \left (t \right )}\right \}, \left \{z \left (t \right ) = c_{1}+\int \frac {-x \left (t \right )^{5}-2 \left (\frac {d}{d t}x \left (t \right )\right ) x \left (t \right )^{2}+2 x \left (t \right )^{3}+\frac {d^{2}}{d t^{2}}x \left (t \right )}{x \left (t \right )^{3}-\frac {d}{d t}x \left (t \right )+x \left (t \right )}d t\right \}\right ]\right \}\]