\[ \left \{x'(t)=h (a-x(t)) (c-x(t)-y(t)),y'(t)=k (b-y(t)) (c-x(t)-y(t))\right \} \] ✓ Mathematica : cpu = 0.34347 (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 = 0.527 (sec), leaf count = 180
\[\left [\{x \relax (t ) = a\}, \left \{y \relax (t ) = \frac {\left (c -a \right ) {\mathrm e}^{k \left (t +c_{1}\right ) \left (-c +a +b \right )}-b}{-1+{\mathrm e}^{k \left (t +c_{1}\right ) \left (-c +a +b \right )}}\right \}\right ]\]