\[ \left \{x'(t)=h (a-x(t)) (c-x(t)-y(t)),y'(t)=k (b-y(t)) (c-x(t)-y(t))\right \} \] ✓ Mathematica : cpu = 0.311989 (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 = 3.299 (sec), leaf count = 180
\[ \left \{ [ \left \{ x \left ( t \right ) =a \right \} , \left \{ y \left ( t \right ) ={\frac { \left ( c-a \right ) {{\rm e}^{k \left ( t+{\it \_C1} \right ) \left ( -c+a+b \right ) }}-b}{-1+{{\rm e}^{k \left ( t+{\it \_C1} \right ) \left ( -c+a+b \right ) }}}} \right \} ],[ \left \{ x \left ( t \right ) ={\it RootOf} \left ( -\int ^{{\it \_Z}}\!{\frac {1}{{\it \_a}-a} \left ( \left ( {\it \_a}-a \right ) ^{-{\frac {k}{h}}}h{\it \_a}+ \left ( {\it \_a}-a \right ) ^{-{\frac {k}{h}}}hb- \left ( {\it \_a}-a \right ) ^{-{\frac {k}{h}}}hc+{\it \_C1} \right ) ^{-1} \left ( \left ( {\it \_a}-a \right ) ^{{\frac {k}{h}}} \right ) ^{-1}}{d{\it \_a}}+t+{\it \_C2} \right ) \right \} , \left \{ y \left ( t \right ) ={\frac {-{\frac {\rm d}{{\rm d}t}}x \left ( t \right ) + \left ( x \left ( t \right ) \right ) ^{2}h+ \left ( -c-a \right ) hx \left ( t \right ) +ach}{h \left ( a-x \left ( t \right ) \right ) }} \right \} ] \right \} \]