\[ \left \{x'(t)=h (a-x(t)) (c-x(t)-y(t)),y'(t)=k (b-y(t)) (c-x(t)-y(t))\right \} \] ✗ Mathematica : cpu = 250.038 (sec), leaf count = 0 , could not solve
DSolve[{Derivative[1][x][t] == h*(a - x[t])*(c - x[t] - y[t]), Derivative[1][y][t] == k*(b - y[t])*(c - x[t] - y[t])}, {x[t], y[t]}, t]
✓ Maple : cpu = 0.673 (sec), leaf count = 180
\[ \left \{ [ \left \{ x \left ( t \right ) =a \right \} , \left \{ y \left ( t \right ) ={\frac { \left ( c-a \right ) {{\rm e}^{k \left ( t+{\it \_C1} \right ) \left ( -c+a+b \right ) }}-b}{-1+{{\rm e}^{k \left ( t+{\it \_C1} \right ) \left ( -c+a+b \right ) }}}} \right \} ],[ \left \{ x \left ( t \right ) ={\it RootOf} \left ( -\int ^{{\it \_Z}}\!{\frac {1}{{\it \_a}-a} \left ( \left ( {\it \_a}-a \right ) ^{-{\frac {k}{h}}}h{\it \_a}+ \left ( {\it \_a}-a \right ) ^{-{\frac {k}{h}}}hb- \left ( {\it \_a}-a \right ) ^{-{\frac {k}{h}}}hc+{\it \_C1} \right ) ^{-1} \left ( \left ( {\it \_a}-a \right ) ^{{\frac {k}{h}}} \right ) ^{-1}}{d{\it \_a}}+t+{\it \_C2} \right ) \right \} , \left \{ y \left ( t \right ) ={\frac {-{\frac {\rm d}{{\rm d}t}}x \left ( t \right ) + \left ( x \left ( t \right ) \right ) ^{2}h+ \left ( -a-c \right ) hx \left ( t \right ) +ach}{h \left ( a-x \left ( t \right ) \right ) }} \right \} ] \right \} \]