Theory of Differential Equations volume 2
Theory of Differential Equations volume 2
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In our eReader you can find the full English version of the book. Read Theory of Differential Equations volume 2 Online - link to read the book on full screen. Our eReader also allows you to upload and read Pdf, Txt, ePub and fb2 books. In the Mini eReder on the page below you can quickly view all pages of the book - Read Book Theory of Differential Equations volume 2
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When the equation is in this form, it is known that a finite number of operations is sufficient to transform it to the preceding case, these operations being transformations of the type The last of the dependent variables v thus arising is that which occurs in the preceding investigation ; it has been expressed as an absolutely converging power-series. When the successive substi tutions are carried out, so as to give the initial dependent variable, the result manifestly is to give a regular fun...ction of t, that vanishes with t and, owing to its construction, satisfies the differential equation. Hence we have the theorem : F. II. 10 146 NON-REGULAR INTEGRALS OF THE [64.
The differential equation dv t-j7 = at where the coefficient a is not a positive integer, possesses a regular integral which vanishes when t = and exists over a finite part of the region of existence of the function fa(v, t).
The argument of 12 may be applied, or a proof similar to that in 13 may be constructed, to shew that the regular integral thus obtained is the only regular integral which vanishes with t and satisfies the equation.
What to read after Theory of Differential Equations volume 2?
You can find similar books in the "Read Also" column, or choose other free books by Forsyth, Andrew Russell, 1858-1942 to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
When the equation is in this form, it is known that a finite number of operations is sufficient to transform it to the preceding case, these operations being transformations of the type The last of the dependent variables v thus arising is that which occurs in the preceding investigation ; it has been expressed as an absolutely converging power-series. When the successive substi tutions are carried out, so as to give the initial dependent variable, the result manifestly is to give a regular fun...ction of t, that vanishes with t and, owing to its construction, satisfies the differential equation. Hence we have the theorem : F. II. 10 146 NON-REGULAR INTEGRALS OF THE [64.
The differential equation dv t-j7 = at where the coefficient a is not a positive integer, possesses a regular integral which vanishes when t = and exists over a finite part of the region of existence of the function fa(v, t).
The argument of 12 may be applied, or a proof similar to that in 13 may be constructed, to shew that the regular integral thus obtained is the only regular integral which vanishes with t and satisfies the equation.
What to read after Theory of Differential Equations volume 2?
You can find similar books in the "Read Also" column, or choose other free books by Forsyth, Andrew Russell, 1858-1942 to read onlineMoreLess
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