We will consider the Banach space valued differential equation eta'(t) = A eta(t), where A is an n x n complex matrix. We give a necessary and sufficient condition in order that the equation have the Hyers-Ulam stability. As a Corollary, we prove that the Banach space valued linear differential equation with constant coefficients y((n))(t) + a(n-1)y((n-1))(t) + ... + a(1)y'(t) + a(0)y(t) = 0 has the Hyers-Ulam stability if and only if Re lambda not equal 0 for all the solutions lambda of the equation z(n) + a(n-1)z(n-1) + ... + a(1)z + a(0) = 0.