mid1solns - APPM 2360: Exam 1 7:00pm 8:30pm, September 22,...

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

View Full Document Right Arrow Icon

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

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: APPM 2360: Exam 1 7:00pm 8:30pm, September 22, 2010. ON THE FRONT OF YOUR BLUEBOOK write: (1) your name, (2) your student ID number, (3) recitation section (4) your instructors name, and (5) a grading table. Text books, class notes, and calculators are NOT permitted. A one-page crib sheet is allowed. Problem 1: (20 points) Please solve the following differential equations and IVPs using an ap- propriate method. (a) (3 points) y = cos( t ) y (b) (5 points) y = sin( t )cos( t )( y + 3) y(0)=1 (c) (6 points) y = 3 y + e- 6 t y (0) = 3 (d) (6 points) y = y t +1 + e 2 t ( t + 1) 2 Solution: (a) y = cos( t ) y dy y = cos( t ) dt ln | y | = sin( t ) + C y ( t ) = ke sin ( t ) (b) y = sin( t )cos( t )( y + 3) dy y + 3 = sin( t )cos( t ) ln | y + 3 | = 1 2 sin 2 ( t ) y + 3 = ke 1 2 sin 2 ( t ) y = ke 1 2 sin 2 ( t )- 3 y (0) = 1 1 = k- 3 k = 4 y ( t ) = 4 e 1 2 sin 2 ( t )- 3 Alternate solution (also correct) y ( t ) = 4 e 1 2 e- 1 2 cos 2 ( t )- 3 (c) y = 3 y + e- 6 t y- 3 y = e- 6 t = e R- 3 dt = e- 3 t ( y- 3 y ) e- 3 t = e- 6 t e- 3 t ye- 3 t = e- 9 t- 9 + C y = ke 3 t- e- 6 t 9 y (0) = 3 3 = k- 1 9 k = 28 9 y ( t ) = 28 9 e 3 t- e- 6 t 9 (d) y- y t + 1 = e 2 t ( t + 1) = e R- ( t +1)- 1 dt = e- ln | t +1 | = ( t + 1)- 1 y- y t + 1 = e 2 t ( t + 1) 2 ( t + 1)- 1 ( y- y t + 1 ) = e 2 t ( t + 1) y ( t + 1)- 1 = 1 2 e 2 t ( t + 1)- Z 1...
View Full Document

This note was uploaded on 10/24/2010 for the course APPM 2360 at Colorado.

Page1 / 5

mid1solns - APPM 2360: Exam 1 7:00pm 8:30pm, September 22,...

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

View Full Document Right Arrow Icon
Ask a homework question - tutors are online