HW5 - y 00 + 2 2 xy + ( x 2 + ) y = 0 . valid in the limit...

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MAE 294A / SIO 203A – Introduction to Applied Mathematics I – Fall 2009 Homework # 5 Assigned: November 12 2009 Due: November 19 2009, in class. 1. (10 points) Derive the leading-order asymptotic behavior at x → ±∞ of the solutions to the equation y 000 - 4 xy 0 - 2 y = 0 . (Using the usual method of dominant balance you should be able to get different behaviors at and -∞ ). This is a third order equation, but the method only leads to two different types of behaviors for each limit. 2. (10 points) For the differential equation y 000 + y 00 - x 2 y = 0 find S ( x ) for each of the three independent solutions valid as x → ∞ . 3. (10 points) Determine the two leading order behaviors for the differential equation
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Unformatted text preview: y 00 + 2 2 xy + ( x 2 + ) y = 0 . valid in the limit x , for general (real) values of the parameter . What happens (explain in words what you would do) in the particular case that = 2-1? 4. (10 points) Consider the dierential equation y 00 + x y-xy = 0 for general (real) values of the parameter . Characterize the two solutions for S ( x ) (i.e. the controlling factor of y) in the limit x . Extra credit (5 points): can you get the next term C ( x ) in each case?...
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