\[ \boxed { \left \{ {\frac {\rm d}{{\rm d}t}}x \left ( t \right ) =h \left ( a-x \left ( t \right ) \right ) \left ( c-x \left ( t \right ) -y \left ( t \right ) \right ) ,{\frac {\rm d}{{\rm d}t}}y \left ( t \right ) =k \left ( b-y \left ( t \right ) \right ) \left ( c-x \left ( t \right ) -y \left ( t \right ) \right ) \right \} } \]
Mathematica: cpu = 0 (sec), leaf count = 0 \[ \text {Hanged} \]
Maple: cpu = 0.359 (sec), leaf count = 237 \[ \left \{ [ \left \{ x \left ( t \right ) =a \right \} , \left \{ y \left ( t \right ) =-{\frac {a{{\rm e}^{{\it \_C1}\,ka+{\it \_C1}\,kb-{\it \_C1} \,kc+akt+bkt-ckt}}-c{{\rm e}^{{\it \_C1}\,ka+{\it \_C1}\,kb-{\it \_C1} \,kc+akt+bkt-ckt}}+b}{-1+{{\rm e}^{{\it \_C1}\,ka+{\it \_C1}\,kb-{\it \_C1}\,kc+akt+bkt-ckt}}}} \right \} ],[ \left \{ x \left ( t \right ) ={ \it RootOf} \left ( -\int ^{{\it \_Z}}\!{\frac {1}{{\it \_a}-a} \left ( \left ( {\it \_a}-a \right ) ^{-{\frac {k}{h}}}h{\it \_a}+ \left ( {\it \_a}-a \right ) ^{-{\frac {k}{h}}}hb- \left ( {\it \_a}-a \right ) ^{-{ \frac {k}{h}}}hc+{\it \_C1} \right ) ^{-1} \left ( \left ( {\it \_a}-a \right ) ^{{\frac {k}{h}}} \right ) ^{-1}}{d{\it \_a}}+t+{\it \_C2} \right ) \right \} , \left \{ y \left ( t \right ) ={\frac {x \left ( t \right ) ah-ach- \left ( x \left ( t \right ) \right ) ^{2}h+x \left ( t \right ) ch+{\frac {\rm d}{{\rm d}t}}x \left ( t \right ) }{hx \left ( t \right ) -ha}} \right \} ] \right \} \]