\[ \left \{x'(t)=h (a-x(t)) (c-x(t)-y(t)),y'(t)=k (b-y(t)) (c-x(t)-y(t))\right \} \] ✓ Mathematica : cpu = 0.399006 (sec), leaf count = 557
\[\left \{\left \{y(t)\to b \left (a h-h \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {(h (a-K[1]))^{\frac {k}{h}}}{(a-K[1]) \left (c_1 (a h-h K[1])^{\frac {k}{h}} (h (a-K[1]))^{\frac {k}{h}}-c (h (a-K[1]))^{\frac {k}{h}}+K[1] (h (a-K[1]))^{\frac {k}{h}}+b (a h-h K[1])^{\frac {k}{h}}\right )}dK[1]\& \right ][-h t+c_2]\right ){}^{\frac {k}{h}} \left (h \left (a-\text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {(h (a-K[1]))^{\frac {k}{h}}}{(a-K[1]) \left (c_1 (a h-h K[1])^{\frac {k}{h}} (h (a-K[1]))^{\frac {k}{h}}-c (h (a-K[1]))^{\frac {k}{h}}+K[1] (h (a-K[1]))^{\frac {k}{h}}+b (a h-h K[1])^{\frac {k}{h}}\right )}dK[1]\& \right ][-h t+c_2]\right )\right ){}^{-\frac {k}{h}}+c_1 \left (a h-h \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {(h (a-K[1]))^{\frac {k}{h}}}{(a-K[1]) \left (c_1 (a h-h K[1])^{\frac {k}{h}} (h (a-K[1]))^{\frac {k}{h}}-c (h (a-K[1]))^{\frac {k}{h}}+K[1] (h (a-K[1]))^{\frac {k}{h}}+b (a h-h K[1])^{\frac {k}{h}}\right )}dK[1]\& \right ][-h t+c_2]\right ){}^{\frac {k}{h}},x(t)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {(h (a-K[1]))^{\frac {k}{h}}}{(a-K[1]) \left (c_1 (a h-h K[1])^{\frac {k}{h}} (h (a-K[1]))^{\frac {k}{h}}-c (h (a-K[1]))^{\frac {k}{h}}+K[1] (h (a-K[1]))^{\frac {k}{h}}+b (a h-h K[1])^{\frac {k}{h}}\right )}dK[1]\& \right ][-h t+c_2]\right \}\right \}\] ✓ Maple : cpu = 0.655 (sec), leaf count = 180
\[\left \{\left [\{x \left (t \right ) = a\}, \left \{y \left (t \right ) = \frac {-b +\left (-a +c \right ) {\mathrm e}^{\left (c_{1}+t \right ) \left (a +b -c \right ) k}}{{\mathrm e}^{\left (c_{1}+t \right ) \left (a +b -c \right ) k}-1}\right \}\right ], \left [\left \{x \left (t \right ) = \RootOf \left (c_{2}+t -\left (\int _{}^{\textit {\_Z}}\frac {\left (\textit {\_a} -a \right )^{-\frac {k}{h}}}{\left (\textit {\_a} h \left (\textit {\_a} -a \right )^{-\frac {k}{h}}+b h \left (\textit {\_a} -a \right )^{-\frac {k}{h}}-c h \left (\textit {\_a} -a \right )^{-\frac {k}{h}}+c_{1}\right ) \left (\textit {\_a} -a \right )}d \textit {\_a} \right )\right )\right \}, \left \{y \left (t \right ) = \frac {a c h +h x \left (t \right )^{2}+\left (-a -c \right ) h x \left (t \right )-\frac {d}{d t}x \left (t \right )}{\left (a -x \left (t \right )\right ) h}\right \}\right ]\right \}\]