**9**, 3, pp. 365-397, 1961

### Uogólnione Równania N-go Rzędu Riccatiego Drugiego Rodzaju. Zastosowania w Teorii Sprężystości

assumptions (only those of continuity of coefficients). In Sec. 1 Rn - equations are defined and several theorems are proved, concerning the properties of these equations and also their connection with the Ln+1 equations corresponding to Rn. Sec. 2 explains the role of Rn - equations in the problem of resolution of the linear differential equation Ln+1[y] into a product of operator factors. Sec. 3 contains a discussion of some applications of the theory of R, equations to the theory of linear equations. Sec. 4 brings a definition of the so called elementarly resolvable equations (the E-class). The E-class, to which belong, as the simplest particular cases, the equations with constant coefficients and the Euler equations, constitutes a natural generalization of the letter class. A general method is given for reducing the order of an E-class equation. Theoretical results are illustrated by examples.

Section 5 contains an accurate solution of the problem of an elastic beam with variable cross-section described by the function (5.2) and acted on by an arbitrary vertical load depending on x and a compressive axial force P.

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