Hostname: page-component-586b7cd67f-g8jcs Total loading time: 0 Render date: 2024-11-28T09:44:49.039Z Has data issue: false hasContentIssue false
  • English
  • Français

A Class of Homogeneous Linear Differential Equations of the Second Order

Published online by Cambridge University Press:  03 November 2016

F. Underwood
Get access Rights & Permissions [Opens in a new window]

Extract

1. In a recent paper Mammana considered the equation

z″ + pz′ + qz = 0,.....(1)

where x is the independent variable and p and q are functions of x, real, finite and continuous in the interval (a, b), and investigated the possibilities of its decomposition into the form

(D + α)(D + β)z = 0,.....(2)

where D ≡ d/dx and α and β are functions of x.

Type
Research Article
Information
The Mathematical Gazette , Volume 16 , Issue 218 , May 1932 , pp. 122 - 125
Copyright
Copyright © Mathematical Association 1932

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

page no 122 note * Mammana, G., “Sopra un nuovo metodo di studio delle equazioni differenziali lineari”, Math. Zeit, 25 (1926), 734–748 CrossRefGoogle Scholar. This work is continued and extended to equations of the nth. order in a more recent paper, “Decomposizione delle espressioni differenziali lineari omogenee in prodotti di fattori simbolici e applicazione relativa allo studio delle equazioni differenziali lineari”, Math. Zeit., 33 (1931), 186-231.

page no 123 note * It will be seen, of course, that the first class is merely that special case of the second for which c = 0, but it seemed to be worthy of separate consideration.

page no 124 note * The fourth class reduces to the first when ψ = 0, and to the second when ψ = c.