Midterm2practice - y ( x ) = e x g ( x ). To further...

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NAME: Math 385 — Midterm 2 practice Total points: 100 . Please explain all answers. Calculators, computers, books and notes are not allowed. Suggestion: even if you cannot complete a problem, write out the part of the solution you know. You can get partial credit for it. 1. [25 points] Calculate (so don’t give me a memorized answer for) the Fouries series expansion for f ( t ) = 2 + t in - 2 t 2. (Note that f ( t ) - 2 is an odd function.) 1
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NAME: 2. [25 points] Find all eigenvalues and associated eigenfunctions for the following boundary value problem for y ( x ): y 00 - 2 y 0 + λy = 0 y (0) = y (2) = 0 You may want to consider the substitution
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Unformatted text preview: y ( x ) = e x g ( x ). To further simplify things you may also want to define μ = λ plus (or minus) an ap-propriate constant. (But your final answer has to be in terms of y ( x ) and λ ) 2 NAME: 3. [25 points] Find the general solution of this forced mechanical oscillator. What will happen to the solution as t → + ∞ ? Does this result depends on initial conditions and why? x 00 + 2 x + 7 x = 2 sin (3 t ) 3 NAME: 4. [25 points] Find the general solution of the following ODE for y ( x ): y 00-6 y + 8 y = 8 x 2 + 1 4...
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This note was uploaded on 01/22/2011 for the course CS 225 taught by Professor Staff during the Spring '08 term at University of Illinois, Urbana Champaign.

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Midterm2practice - y ( x ) = e x g ( x ). To further...

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