Question: writing dirac_delta code in maple

Hi

How can I write and solve a dirac_delta function in maple, for example in below equations:

F[0]:=0;
F[1]:=a;
F[2]:=b;

eq1:=sum((k-m+2)*(k-m+1)*F[k-m+2]*Dirac[m-1], m = 0 .. k);

eq2:=(k+1)*F[k+1]-Dirac[k];

for k from 0 to 10 do
F[k+3]:=solve(F[k+3]=(eq1+eq2)/((k+3)*(k+2)*(k+1)),F[k+3]);
end do;

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