{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

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

This preview shows pages 1–3. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

{[ snackBarMessage ]}

### Page1 / 5

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

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online