restart:
sys:= diff(x(t),t)=x(t)-2*y(t)-z(t), diff(y(t),t)=x(t)+y(t)+z(t), diff(z(t),t)=x(t)-z(t);
gensol:=dsolve({sys},{x(t),y(t),z(t)});
init:=x(0)=0, y(0)=1, z(0)=2;
parsol:=dsolve({sys,init},{x(t),y(t),z(t)});
x1:=rhs(parsol[1]); y1 := rhs(parsol[1]); z1 := rhs(parsol[1]);

Вроде так...