Homework-6-f11

# Homework-6-f11 - ² 2 ± ′′ − ² ² 3 ± ′ ² 3 ±...

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1 AMS 361: Applied Calculus IV by Prof Y. Deng Homework 6 Assignment Date: Thursday (10/20/2011) Collection Date: Thursday (11/03/2011) Grade: Each problem is worth 10 points. Problem 6.1 Find the general solution of the following equation ( ° − 3) 3 ( ° − 2) 2 ( ° 2 2 ° + 2) ± ( ² ) = 0 where ° ≡ ³ ³² Problem 6.2 Find the general solution of the following equation ² ³ ³² − ´µ ± ( ² ) = 0 where ´ = constant and · = positive integer Problem 6.3 Find the general solution of the following Euler-Cauchy equation ² 2 ± ′′ 5 ²± + 13 ± = 0 ∀² > 0 Problem 6.4 Find the general solution for the following equation,
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Unformatted text preview: ² 2 ± ′′ − ² ( ² + 3) ± ′ + ( ² + 3) ± = 0 ∀² > − 1 given ± 1 ( ² ) = ² Problem 6.5 Find the particular solution for (with constants ¸ , ¸ ) ± ′′ + ¸ 2 ± = cos( ¸ ² ) sin( ¸ ² ) Hint : Naturally, it is very tedious to find the closed-form solution for this equation. Luckily, the main purpose of this problem is to understand the “vibrational principles” and thus you may express your solution in an integral form, if necessary. Problem 6.6 Find the particular solution for ± ′′′ + ± ′′ + ± ′ + ± = 1 + sin ² + cos 2 ² + ¹ º...
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## This note was uploaded on 11/14/2011 for the course AMS 361 taught by Professor Staff during the Fall '08 term at SUNY Stony Brook.

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