N:=10;
y[-1]:=t->1;
for i from 0 to N do
  c:='c';r:=int(-y[i-1](t-1),t)+c;
  rr:=unapply(r,t);
  c:=solve(rr(i)=y[i-1](i),c);
  y[i]:=unapply(r,t);
od;
for i from -1 to N do
  P[i]:=plot(y[i](t),t=i..i+1);
od;
plots[display](seq(P[j],j=-1..N));