Hi,
try this:
NDSolve[{x'[t] == 0.5 x[t] y[t] (1 + x[t]) (2 - x[t]), y'[t] == x[t]^2 (y[t]^2) - 0.5 (y[t]^2) (x[t] + 1) (x[t] + 2), x[0] == 4, y[0] == 10000}, {x, y}, {t, 0, 1000}]
You should use the [ ] only for functions. If you want to set normal parenthesis, use ( ).
Plotting the result
Plot[{x[t] /. sols, y[t] /. sols}, {t, 0, 10}]
gives
Cheers,
Marco.
