\[ \left \{x'(t)=x(t) (a (p x(t)+q y(t))+\alpha ),y'(t)=y(t) (b (p x(t)+q y(t))+\beta )\right \} \] ✗ Mathematica : cpu = 965.002 (sec), leaf count = 0 , could not solve
DSolve[{Derivative[1][x][t] == x[t]*(alpha + a*(p*x[t] + q*y[t])), Derivative[1][y][t] == y[t]*(beta + b*(p*x[t] + q*y[t]))}, {x[t], y[t]}, t]
✓ Maple : cpu = 9.725 (sec), leaf count = 147
\[ \left \{ [ \left \{ x \left ( t \right ) =0 \right \} , \left \{ y \left ( t \right ) ={\frac {\beta }{{{\rm e}^{-\beta \,t}}{\it \_C1}\,\beta -bq}} \right \} ],[ \left \{ x \left ( t \right ) ={\it ODESolStruc} \left ( {\it \_b} \left ( {\it \_a} \right ) ,[ \left \{ \left ( \left ( {\frac {\rm d}{{\rm d}{\it \_a}}}{\it \_b} \left ( {\it \_a} \right ) \right ) \left ( {\it \_b} \left ( {\it \_a} \right ) \right ) ^{{\frac {-a-b}{a}}}- \left ( {\it \_b} \left ( {\it \_a} \right ) \right ) ^{-{\frac {b}{a}}} \left ( ap{\it \_b} \left ( {\it \_a} \right ) +\alpha \right ) \right ) {{\rm e}^{-{\frac {{\it \_a}\, \left ( \beta \,a-\alpha \,b \right ) }{a}}}}+{\it \_C1}=0 \right \} , \left \{ {\it \_a}=t,{\it \_b} \left ( {\it \_a} \right ) =x \left ( t \right ) \right \} , \left \{ t={\it \_a},x \left ( t \right ) ={\it \_b} \left ( {\it \_a} \right ) \right \} ] \right ) \right \} , \left \{ y \left ( t \right ) ={\frac {- \left ( x \left ( t \right ) \right ) ^{2}ap-\alpha \,x \left ( t \right ) +{\frac {\rm d}{{\rm d}t}}x \left ( t \right ) }{qx \left ( t \right ) a}} \right \} ] \right \} \]