This preview shows pages 1–4. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Math 20D, Sample Midterm 2 Solutions November 11, 2006 Name: Section: This exam consists of 6 pages including this front page. Ground Rules 1. No calculator is allowed. 2. Show your work for every problem. A correct answer without any justification will receive no credit. 3. You may use one 4by6 index card, both sides. Score 1 10 2 10 3 10 4 10 5 10 Total 50 1 1. (a) Solve y 00 4 y + 4 y = 0 . The characteristic equation r 2 4 r + 4 = 0 gives r = 2. Thus y = C 1 e 2 t + C 2 te 2 t . (b) Solve y 00 + y + y = 0 The characteristic equation r 2 + r + 1 = 0 gives r = 1 i 3 2 Thus y = C 1 e 1 / 2 t cos( 3 2 t ) + C 2 e 1 / 2 t sin( 3 2 t ) . 2 2. Consider t 2 y 00 4 ty + 6 y = 0. First verify that y = t 2 is a solution. Then find the general solution by the method of reduction of order. t 2 ( t 2 ) 00 4 t ( t 2 ) + 6 t 2 = 2 t 2 8 t 2 + 6 t 2 = 0 . Thus y = t 2 is indeed a solution....
View Full
Document
 Spring '06
 Mohanty
 Math

Click to edit the document details