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Final2practice

# 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 - 1 x 2 = 0; y (1) = y (1) = 0 2
NAME: 3. [15 points] Find the general solutions of the following ODE’s for y ( x ): a) y = 4 y b) y = y sin ( x ) c) y + 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 - 2 y + 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
NAME: 5. [10 points] Calculate the Fourier series expansion for the following func- tion of period 2: f ( t ) = 2 + 2 t 2 for - 1 < t < 1 5

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NAME: 6. [15 points] Find the solution y ( x, t ) in 0 < x < 3 and t 0 for the following heat conduction problem:

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

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