 Solution

For a constant-coefficient differential operator $P(D)={\sum }_{|\beta |\le m}{a}_{\beta }{D}^{\beta }$, a hypersurface with nonzero normal covector $\nu$ is a non-characteristic hypersurface precisely when its principal symbol $P_m(\nu )={\sum }_{|\beta |=m}{a}_{\beta }{\nu }^{\beta }$ is nonzero. Multiplying the symbol by the conventional factor $i^m$ does not affect this criterion. For the initial line here the normal is $(0,1)$.