hw1key - AMATH 351 Homework 1 Section1.1 15,16,17,18,19,20...

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Unformatted text preview: AMATH 351 Homework 1 Section1.1 15,16,17,18,19,20 Section1.3 1,2,3,4,5,6,13,14,17,19 Section2.2 6,18,32 *For gures and Problem 30, download them on the course webpage In each of the following problem verify that each given function is a solution of the di erential equation. 13. y 00 + y = sec t, < t < π/ 2; y = (cos t ) ln cos t + t sin t y = cos t ln(cos t ) + t sin t y =- sin t ln(cos t ) + cos t 1 cos t (- sin t ) + sin t + t cos t =- sin t ln(cos t ) + t cos t y 00 =- cos t ln(cos t ) + sin t 1 cos t sin t + cos t- t sin t = ⇒ y 00 + y =- cos t ln(cos t ) + sin 2 t cos t + cos t- t sin t + cos t ln(cos t ) + t sin t = sin 2 t + cos 2 t cos t = 1 cos t = sec t (0 < t < π 2 ) 14. y- 2 ty = 1; y = e t 2 ´ t e- s 2 ds + e t 2 y = e t 2 ˆ t e- s 2 ds + e t 2 y = 2 te t 2 ˆ t e- s 2 ds + e t 2 e- t 2 + 2 te t 2 y- 2 ty = 2 te t 2 ˆ t e- s 2 ds + 1 + 2 te t 2- 2 te t 2 ˆ t e- s 2 ds- 2 te t 2 = 1 1 In the following problem determing the value of r for which the given di erential equation has solutions of the form...
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This note was uploaded on 01/10/2010 for the course MATH 124 taught by Professor Walker during the Spring '08 term at University of Washington.

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hw1key - AMATH 351 Homework 1 Section1.1 15,16,17,18,19,20...

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