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In this article, the equivalence and symmetries of underdetermined differential equations and differential equations with deviations of the first order are considered with respect to the pseudogroup of transformations $\overline{x}=\varphi \left(x\right),$ $\overline{y}=\overline{y}\left(\overline{x}\right)=L\left(x\right)y\left(x\right).$ That means, the transformed unknown function $\overline{y}$ is obtained by means of the change of the independent variable and subsequent multiplication by a nonvanishing factor. Instead of the common direct calculations, we use some more advanced tools from differential geometry;...