Mathematica is case sensitive and built-in symbols are always capitalized.
Don't use capital D for your own symbol by the way.
With corrected syntax:
DSolve[{e*t''''[x] + d*t''[x] - v*t'[x] == k*t[x], t'[0] == 0, t'[L] == 0, t''[0] == 0, t''[L] == 0}, t[x], x]
(* {{t[x] -> 0}} *)
Gives only a trivial solution.
Regards M.I.
