ImplicitLMM:=proc(k)
local i,j,a,b,eqns;
  a[k]:=1;
  eqns:={sum(a[i],i=0..k),seq(sum(a[i]*i^j,i=0..k)=
         j*sum(b[i]*i^(j-1),i=0..k),j=1..2*k)};
  solve(eqns,indets(eqns)); assign(%);
  sum(a[k-j]*y[k-j],j=0..k)= dt*sum(b[k-j]*f[k-j],j=0..k);
end: