\[ \left \{x'(t)=x(t) (a y(t)+b),y'(t)=y(t) (c x(t)+d)\right \} \] ✓ Mathematica : cpu = 0.28613 (sec), leaf count = 204
\[\left \{\left \{y(t)\to \frac {b W\left (\frac {a \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {1}{K[1] \left (W\left (\frac {a e^{\frac {c_1}{b}+\frac {c K[1]}{b}} K[1]^{\frac {d}{b}}}{b}\right )+1\right )}dK[1]\& \right ][b t+c_2]{}^{\frac {d}{b}} \exp \left (\frac {c \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {1}{K[1] \left (W\left (\frac {a e^{\frac {c_1}{b}+\frac {c K[1]}{b}} K[1]^{\frac {d}{b}}}{b}\right )+1\right )}dK[1]\& \right ][b t+c_2]}{b}+\frac {c_1}{b}\right )}{b}\right )}{a},x(t)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {1}{K[1] \left (W\left (\frac {a e^{\frac {c_1}{b}+\frac {c K[1]}{b}} K[1]^{\frac {d}{b}}}{b}\right )+1\right )}dK[1]\& \right ][b t+c_2]\right \}\right \}\] ✓ Maple : cpu = 0.46 (sec), leaf count = 92
\[[\{x \relax (t ) = 0\}, \{y \relax (t ) = c_{1} {\mathrm e}^{d t}\}]\]