HW6 - MAE 294A / SIO 203A Introduction to Applied...

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MAE 294A / SIO 203A – Introduction to Applied Mathematics I – Fall 2009 Homework # 6 Assigned: November 19 2009 Due: December 1 2009, in class. 1. (10 points) Consider the parabolic cylinder equation y ′′ + p ν + 1 2 1 4 x 2 P y = 0 , for a real parameter ν . Derive the asymptotic behavior of the two solutions of the equation for x + . 2. (10 points) What is the leading order behavior of the solutions to y ′′ + x 3 / 2 y x 2 y = 0 , as x + ? Show that is is inconsistent to assume that S ′′ S 2 . However show that the approximate equation S ′′ + ( S ) 2 x 2 can be solved exactly by assuming a solution of the form S = c/x . 3. (10 points) Find the leading-order behavior to y y x = cos x, as x 0 + . Compare the leading-order behavior with the exact solution to the equation. 4. (10 points) Find the ±rst three terms in the local behavior as x 0 + of the particular solution to
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This note was uploaded on 03/16/2010 for the course MAE 294b taught by Professor Young,w during the Fall '08 term at UCSD.

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