Some properties of linear homogeneous transformation of independent variable in ordinary differential linear equations

summary:The article studies a general linear differential equations of the 2nd order the solution $y(t)$ of which generates an orthogonal sequence $y(k_it)$ where $k_i$ is a suitably ordered sequence of positive roots of the solution $y(t)$. Actually differential equations of Euler's type are dealt with. Further a certain generalization concerning the general solution of certain iterated equation of the 4th order is given