\[ \left \{x'(t)=x(t) (a y(t)+b),y'(t)=y(t) (c x(t)+d)\right \} \] ✓ Mathematica : cpu = 0.700961 (sec), leaf count = 198
\[\left \{\left \{y(t)\to \frac {b W\left (\frac {a \text {InverseFunction}\left [\int _1^{\text {$\#$1}} \frac {1}{K[1] \left (W\left (\frac {a e^{\frac {c K[1]}{b}+\frac {c_1}{b}} K[1]^{\frac {d}{b}}}{b}\right )+1\right )} \, dK[1]\& \right ]\left [b t+c_2\right ]{}^{\frac {d}{b}} \exp \left (\frac {c \text {InverseFunction}\left [\int _1^{\text {$\#$1}} \frac {1}{K[1] \left (W\left (\frac {a e^{\frac {c K[1]}{b}+\frac {c_1}{b}} K[1]^{\frac {d}{b}}}{b}\right )+1\right )} \, dK[1]\& \right ]\left [b t+c_2\right ]+c_1}{b}\right )}{b}\right )}{a},x(t)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}} \frac {1}{K[1] \left (W\left (\frac {a e^{\frac {c K[1]}{b}+\frac {c_1}{b}} K[1]^{\frac {d}{b}}}{b}\right )+1\right )} \, dK[1]\& \right ]\left [b t+c_2\right ]\right \}\right \}\]
✓ Maple : cpu = 0.497 (sec), leaf count = 92
\[ \left \{ [ \left \{ x \left ( t \right ) =0 \right \} , \left \{ y \left ( t \right ) ={\it \_C1}\,{{\rm e}^{dt}} \right \} ],[ \left \{ x \left ( t \right ) ={\it RootOf} \left ( -\int ^{{\it \_Z}}\!{\frac {1}{{\it \_a}\,b} \left ( {\it lambertW} \left ( {\frac {{{\rm e}^{-1}}}{b}{{\rm e}^{{\frac {c{\it \_a}}{b}}}}{{\it \_a}}^{{\frac {d}{b}}}{{\rm e}^{{\frac {{\it \_C1}}{b}}}}} \right ) +1 \right ) ^{-1}}{d{\it \_a}}+t+{\it \_C2} \right ) \right \} , \left \{ y \left ( t \right ) ={\frac {-bx \left ( t \right ) +{\frac {\rm d}{{\rm d}t}}x \left ( t \right ) }{ax \left ( t \right ) }} \right \} ] \right \} \]