\[ \boxed { \left \{ {\frac {\rm d}{{\rm d}t}}x \left ( t \right ) =x \left ( t \right ) \left ( a \left ( px \left ( t \right ) +qy \left ( t \right ) \right ) +\alpha \right ) ,{\frac {\rm d}{{\rm d}t}}y \left ( t \right ) =y \left ( t \right ) \left ( \beta +b \left ( px \left ( t \right ) +qy \left ( t \right ) \right ) \right ) \right \} } \]
Mathematica: cpu = 0 (sec), leaf count = 0 \[ \text {Hanged} \]
Maple: cpu = 13.791 (sec), leaf count = 181 \[ \left \{ [ \left \{ x \left ( t \right ) =0 \right \} , \left \{ y \left ( t \right ) ={\frac {\beta }{{{\rm e}^{-\beta \,t}}{\it \_C1}\,\beta -bq}} \right \} ],[ \left \{ x \left ( t \right ) ={\it ODESolStruc} \left ( { \it \_b} \left ( {\it \_a} \right ) ,[ \left \{ \left ( {\it \_b} \left ( {\it \_a} \right ) \right ) ^{-{\frac {a+b}{a}}}{{\rm e}^{-{\frac {{ \it \_a}\, \left ( a\beta -\alpha \,b \right ) }{a}}}}{\frac {\rm d}{ {\rm d}{\it \_a}}}{\it \_b} \left ( {\it \_a} \right ) -{\it \_b} \left ( {\it \_a} \right ) {{\rm e}^{-{\frac {{\it \_a}\, \left ( a\beta -\alpha \,b \right ) }{a}}}} \left ( {\it \_b} \left ( {\it \_a} \right ) \right ) ^{-{\frac {b}{a}}}ap-{{\rm e}^{-{\frac {{\it \_a}\, \left ( a \beta -\alpha \,b \right ) }{a}}}} \left ( {\it \_b} \left ( {\it \_a} \right ) \right ) ^{-{\frac {b}{a}}}\alpha +{\it \_C1}=0 \right \} , \left \{ {\it \_a}=t,{\it \_b} \left ( {\it \_a} \right ) =x \left ( t \right ) \right \} , \left \{ t={\it \_a},x \left ( t \right ) ={\it \_b} \left ( {\it \_a} \right ) \right \} ] \right ) \right \} , \left \{ y \left ( t \right ) ={\frac {- \left ( x \left ( t \right ) \right ) ^{2}ap -\alpha \,x \left ( t \right ) +{\frac {\rm d}{{\rm d}t}}x \left ( t \right ) }{qx \left ( t \right ) a}} \right \} ] \right \} \]