Accession Number:

AD0408289

Title:

ON THE SOLUTIONS OF THE DIFFERENTIAL EQUATION Y SUB VI = XY. I. ANALYSIS

Descriptive Note:

Corporate Author:

BROWN UNIV PROVIDENCE RI DIV OF APPLIED MATHEMATICS

Personal Author(s):

Report Date:

1963-05-01

Pagination or Media Count:

28.0

Abstract:

The differential equation y to the power of vi xy plays an important role in the asymptotic treatment of the stability of viscous flow between contra-rotating cylinders and, in one limiting case, solutions of this equation are required that remain bounded as x approaches plus infinity. A set of standard solutions have therefore been defined such that three of them, denoted by Akx, are bounded as x approaches plus infinity, while the remaining three solutions, denoted by Bkx, are unbounded as x approaches plus infinity. The contour integral representations of these solutions are given, together with their power-series and asymptotic expansions. It is also shown that a slightly modified set of these solutions provide a numerically satisfactory set over the entire interval minus infinity is less than x is less than plus infinity.

Subject Categories:

  • Theoretical Mathematics
  • Fluid Mechanics

Distribution Statement:

APPROVED FOR PUBLIC RELEASE