ON THE SOLUTIONS OF THE DIFFERENTIAL EQUATION Y SUB VI = XY. I. ANALYSIS
BROWN UNIV PROVIDENCE RI DIV OF APPLIED MATHEMATICS
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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.
- Theoretical Mathematics
- Fluid Mechanics