ON THE SOLUTIONS OF THE DIFFERENTIAL EQUATION Y SUB VI = XY. I. ANALYSIS
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 Ak(x), are bounded as x approaches plus infinity, while the remaining three solutions, denoted by Bk(x), 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.
Document Details
- Document Type
- Technical Report
- Publication Date
- May 01, 1963
- Accession Number
- AD0408289
Entities
People
- R. L. Duty
- W. H. Reid
Organizations
- Brown University