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# HW3 - nally use Lindstedt-Poincar e method to obtain a...

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Math 401 (Sec. 502) Spring, 2009 Homework 3 (due February 12) Q1. Use Lindstedt-Poincar´ e method to obtain a two-term uniformly valid approximation to the ODE (where 0 < << 1) y 00 + y + y 2 = 0 , y (0) = 1 , y 0 (0) = 0 . Q2. Find the first two terms of the perturbation series solutions to the initial value problems (where 0 < << 1) y 00 + ( a 2 + y 0 2 ) y = 0 , y (0) = 1 , y 0 (0) = 0 , where a is a given constant. Explain why this solution is not uniform. Fi-
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Unformatted text preview: nally, use Lindstedt-Poincar e method to obtain a two-term uniformly valid approximation. Q3. Use Lindstedt-Poincar e method to obtain a two-term uniformly valid approximation to the ODE (where 0 &amp;lt; &amp;lt;&amp;lt; 1) y 00 + (1 + ) y = 0 , y (0) = 0 ,y (0) = 1 ....
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