Dear Kay. You can make sure, that Cv is 5-dimentional function-vector.

Get["<your_path>:\\env.txt"]
Plot[{Cv[[1]], Cv[[2]]}, {t, 0, 1}]

This gives the following:

Other components of Cv are also function-vectors.

Not sure what Cv[[i]] is I thought it's a vector of time dependent functions? If so I would construct the equations this way:

In[7]:= eqns = 
 Join[Table[
   Sum[A[i, j] v[j]''[t] + B[i, j] v[j][t], {j, 1, 4}] == 
    cv[i][t], {i, 1, 4}], Table[v[j][0] == 0, {j, 1, 4}], 
  Table[v[j][1] == 0, {j, 1, 4}]]

Out[7]= {B[1, 1] v[1][t] + B[1, 2] v[2][t] + B[1, 3] v[3][t] + 
   B[1, 4] v[4][t] + A[1, 1] (v[1]^\[Prime]\[Prime])[t] + 
   A[1, 2] (v[2]^\[Prime]\[Prime])[t] + 
   A[1, 3] (v[3]^\[Prime]\[Prime])[t] + 
   A[1, 4] (v[4]^\[Prime]\[Prime])[t] == cv[1][t], 
 B[2, 1] v[1][t] + B[2, 2] v[2][t] + B[2, 3] v[3][t] + 
   B[2, 4] v[4][t] + A[2, 1] (v[1]^\[Prime]\[Prime])[t] + 
   A[2, 2] (v[2]^\[Prime]\[Prime])[t] + 
   A[2, 3] (v[3]^\[Prime]\[Prime])[t] + 
   A[2, 4] (v[4]^\[Prime]\[Prime])[t] == cv[2][t], 
 B[3, 1] v[1][t] + B[3, 2] v[2][t] + B[3, 3] v[3][t] + 
   B[3, 4] v[4][t] + A[3, 1] (v[1]^\[Prime]\[Prime])[t] + 
   A[3, 2] (v[2]^\[Prime]\[Prime])[t] + 
   A[3, 3] (v[3]^\[Prime]\[Prime])[t] + 
   A[3, 4] (v[4]^\[Prime]\[Prime])[t] == cv[3][t], 
 B[4, 1] v[1][t] + B[4, 2] v[2][t] + B[4, 3] v[3][t] + 
   B[4, 4] v[4][t] + A[4, 1] (v[1]^\[Prime]\[Prime])[t] + 
   A[4, 2] (v[2]^\[Prime]\[Prime])[t] + 
   A[4, 3] (v[3]^\[Prime]\[Prime])[t] + 
   A[4, 4] (v[4]^\[Prime]\[Prime])[t] == cv[4][t], v[1][0] == 0, 
 v[2][0] == 0, v[3][0] == 0, v[4][0] == 0, v[1][1] == 0, v[2][1] == 0,
  v[3][1] == 0, v[4][1] == 0}