Maybe this will help you a little
sol=Simplify[{x[t],y[t]}/.DSolve[{x''[t]==b x'[t],y''[t]==-b y'[t]-g,x[0]==0,y[0]==0,x'[0]==v Cos[theta],y'[0]==v Sin[theta]},{x,y},t][[1]]];
yy[t_]:=sol[[2]];yy[t]
xx[t_]:=sol[[1]];xx[t]
which displays
(g*(1-E^(-b*t)-b*t)+b*(1-E^(-b*t))*v*Sin[theta])/b^2
and
((-1+E^(b*t))*v*Cos[theta])/b
