Particular solutions of a Differential Equation not evaluated in a given case

Question

Below first case which gives particular solutions of an OED correctly:

ClearAll[soln];                            (* case 1 *)
soln[a_?NumericQ] := 
soln[a] = 
DSolve[{y''[t] + y[t] == Sin[t], y[0] == a, y'[0] == 0}, y[t], 
 t];     
res1  =  Grid[
Partition[ 
Table [soln[i][[1, 1, 2]], {i, 0, 2, 1}] // FullSimplify , 1], 
 Frame -> All] 

As the OED is manipulated elsewhere in my notebook I need to rewrite the above code using an assignment for the equation:

 ClearAll[solp];                                       (* case 2 *)
 eqd := {y''[t] + y[t] == Sin[t], y[0] == a, y'[0] == 0};
 solp[a_?NumericQ] := solp[a] = DSolve[eqd, y[t], t];     
 res2  =  
 Grid[Partition[ 
 Table [solp[i][[1, 1, 2]], {i, 0, 2, 1}] // FullSimplify , 1], 
 Frame -> All]

However this time I only get the general solution with the particular solutions left unevaluated for the arbitray value "a". What's wrong here?

I checked that it is possible to use an assignement for the equation given to DSolve but after rewriting the first case like that:

solq = DSolve[eqd, y[t], t] ;                 (* case 3 *)
res3  =  Grid[
Partition[ 
Table [solq[[1, 1, 2]] /. a -> i, {i, 0, 2, 1}] // FullSimplify , 
1], Frame -> All]   
res3 == res1 

Why is it OK here and not in case 2? Thanks

Answer 1

This may be a better way to do it:

ClearAll[solp];
(*case 2*)
eqd[a_] := {y''[t] + y[t] == Sin[t], y[0] == a, y'[0] == 0};
solp[a_?NumericQ] := solp[a] = DSolve[eqd[a], y[t], t];
res2 = Grid[
  Partition[Table[solp[i][[1, 1, 2]], {i, 0, 2, 1}] // FullSimplify, 
   1], Frame -> All]