practice exam - MATH 216 Introduction to Differential...

Info iconThis preview shows pages 1–5. 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

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: MATH 216 Introduction to Differential Equations Fall 2007 First Midterm Exam Name Section This examination booklet contains 8 problems on 9 pages. This is a closed book exam. No calculators are allowed. One 3 by 5 note card is allowed. Show all your work. No work, no points! Problem Possible score Your score 1 20 2 13 3 10 4 10 5 10 6 12 7 13 8 12 Total 100 1 1. (10 Points) Solve the equation dy dx = y 1 + x 2 , y (1) = 1 Solution: dy y = dx 1+ x 2 2 pts 2 y = arctan x + c 3 pts 2 = 4 + c 2 pts 2 y = arctan x + 2- 4 y = 1 / 2(arctan x + 2- 4 ) 2 3 pts 2 2. (10 Points) Consider x 2 dy dx + xy = 1 x , y (1) = 1 . (a) Determine the integrating factor ( x ). = x 2 pts (b) Rewrite the differential equation so that the left hand side is a perfect derivative. d ( x y ) dx = 1 x 2 2 pts (c) Solve for y ( x ). Solution: y = 1 x [ R 1 x 2 + C ] y =- 1 /x 2 + C/x y =- 1 /x 2 + 2 /x 6 pts 3 3. (15 Points) Consider the following initial value problem dx dt = 10 x- 5 x 2 x (0) = C (a) (4 pts) Find the equilibrium solutions and determine whether they are stable or not....
View Full Document

This note was uploaded on 04/01/2008 for the course MATH 216 taught by Professor Stenstones? during the Fall '07 term at University of Michigan.

Page1 / 13

practice exam - MATH 216 Introduction to Differential...

This preview shows document pages 1 - 5. Sign up to view the full document.

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