Geodesic
Some properties of linear homogeneous transformation of independent variable in ordinary differential linear equations
Applications of Mathematics, Tome 16 (1971) no. 6, pp. 431-438
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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.
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.
DOI : 10.21136/AM.1971.103378
Classification : 34A25, 34A30, 34B30, 34C20 
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Barvínek, Erich. Some properties of linear homogeneous transformation of independent variable in ordinary differential linear equations. Applications of Mathematics, Tome 16 (1971) no. 6, pp. 431-438. doi: 10.21136/AM.1971.103378

[1] B. G. Korenjev: Some elasticity and heat conduction problems solvable in Bessel functions. (Russian), Moscow 1960.

[2] V. Pane: Die allgemeine Lösung einer zylindrischen Differentialgleichung vierter Ordnung nullten Parameterwertes. Aplikace matematiky, sv. 16 (1971), čís. 3.

[3] A. Gray G. B. Mathews: A treatise on Bessel functions and their applications to physics.

[4] H. Bateman: Higher transcendental functions. Vol. 2. | Zbl

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