HW4 - term Hint See Chapter 5 of our text book or the class...

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Math 401 (Sec. 502) Spring, 2009 Homework 4 (due February 19) Q1. Consider the following IVP (called damped linear oscillator) y ′′ + 2 ǫy + y = 0; y (0) = 0 , y (0) = 1 . (a) Compute the exact solution. (b) Use two-scale perturbation theory to Fnd a leading-order approxima- tion. (c) Then compute the second term of the solution. Do you get any secular term in this second term? If so, then, explain the signiFcance of that secular
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Unformatted text preview: term. [ Hint: See Chapter 5 of our text book or the class notes.] Q2. Use two-scale perturbation theory to Fnd a leading-order approximation to the non-linear ODE: y ′′ + y-ǫ [ y ′-1 3 ( y ′ ) 3 ] = 0; y (0) = 0 , y ′ (0) = 1 . [ Hint: You are given the solution to 2 dx dθ = x-1 4 x 3 , x (0) = 1 is x ( θ ) = 2 √ 1+3 e-θ ]...
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This note was uploaded on 04/27/2009 for the course MATH 401 taught by Professor Sarkar during the Spring '09 term at Texas A&M.

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