  Consider the linear differential equation of $m$-th order with constant
coefficients from the valuation ring $K$ of a non-Archimedean field. We get
sufficient conditions of uniqueness and existence for the solution of this
equation from $K[[x]]$. Also the fundamental solution from
$\frac{1}{x}K[[\frac{1}{x}]]$ of the equation is obtained and it is shown that
the convolution of the fundamental solution and a non-homogeneity is a unique
solution of the equation.
