Let there be given a differential operator on ${ℝ}^n$ of the form $D={\sum }_{i,j=1}^n{a}_{ij}·x_j\partial /\partial x_i+\mu$, where $A=\left(a_{ij}\right)$ is a real matrix and μ is a complex number. We study the following question: To what extent the mapping $D:S^{\text{'}}\left({ℝ}^n\right)\to S^{\text{'}}\left({ℝ}^n\right)$ is surjective? We shall give some conditions on A and μ which assure the surjectivity of D.