Final2practice - NAME: Math 385 Final exam practice Total...

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NAME: Math 385 — Final exam practice Total points: 100 + 15 extra . 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. [15 points] Find the general solution of the following ODE for y ( x ): y (5) - 4 y (4) + 4 y (3) = 0 (where y (4) means the fourth derivative of y ) 1
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NAME: 2. [15 points] Solve the following initial value problem for y ( x ): y 00 - 1 x 2 = 0; y (1) = y 0 (1) = 0 2
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NAME: 3. [15 points] Find the general solutions of the following ODE’s for y ( x ): a) y 00 = 4 y b) y 0 = y sin ( x ) c) y 00 + 2 y = 0 3
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NAME: 4. [15 extra 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 y ( x ) = e x g ( x ). (But your final answer has to be in terms of y ( x )) 4
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5. [10 points]
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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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Final2practice - NAME: Math 385 Final exam practice Total...

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