\[ \left \{x'(t)=x(t) (a (p x(t)+q y(t))+\alpha ),y'(t)=y(t) (b (p x(t)+q y(t))+\beta )\right \} \] ✗ Mathematica : cpu = 300.01 (sec), leaf count = 0
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]
, timed out
$Aborted
✗ Maple : cpu = 0. (sec), leaf count = 0
dsolve({diff(x(t),t) = x(t)*(a*(p*x(t)+q*y(t))+alpha), diff(y(t),t) = y(t)*(beta+b*(p*x(t)+q*y(t)))})
, result contains DESol or ODESolStruc
\[\left [\{x \left (t \right ) = 0\}, \left \{y \left (t \right ) = \frac {\beta }{{\mathrm e}^{-\beta t} c_{1} \beta -b q}\right \}\right ]\]