Get started today!

Good to have you back!
If you've signed in to StudyBlue with Facebook in the past, please do that again.

- StudyBlue
- Michigan
- University of Michigan - Ann Arbor
- Mathematics
- Mathematics 216
- Epstein
- midterm1fall06.pdf

Manas T.

Advertisement

Name: Section/Time of lecture: Professor/GSI: MATH 216 MIDTERM I Each part of a problem counts equally. To get full score you need to carefully explain what you did. No calculators allowed. 1 Problem Points Score 1 30 2 30 3 30 4 60 TOTAL 150 2 Problem 1. a) Verify that the function y(x) = 1x + lnx satisfies x2yprimeprime + 2xyprime ?xy = ?xlnx b) Solve dydx = sinx(cosx)2 + 1x2,y(2pi) = 1. c) Sketch the slope field and solution curves for dydx = ?1?x2 where defined. Include enough detail to be able to give a rough sketch of the solution curves with y(0) = 0 and y(0) = 1. 3 Problem 2. a) Solve dydx = x(1?2y)e2x,y(0) = 2 b) Solve (x2 + 1)yprime = ?3xy + x,y(0) = 0. c) The time rate of change of a population P is proportional to the cube root of P. At time t=0, the population is 1000 and the rate of increase is 100 at that time. What is the population at time t=10? 4 Problem 3. a) Let dxdt = ?5x + 2x3. Find the equilibrium solutions. Which ones are stable? b) Suppose that a motor boat is moving at 100 m/s when the motor quits. After 20 seconds, the boat has slowed to 10 m/s. Assume the resistance is proportional to its speed. Hence we have the differential equation for the speed v : dv dt = ?kv. How far will the boat coast? c) Use Euler with stepsize .5 to estimate y(2) for dydx = x2 + y3,y(1) = 0. 5 Problem 4. a) Solve the equation yprimeprime ?3yprime ?10 = 0 with initial conditions y(0) = 3,yprime(0) = ?1. b) Solve the equation 5z2 ?2z + 10 = 0. c) Solve 9yprimeprime + 6yprime + 25y = 0,y(0) = 2,yprime(0) = 1 6

Advertisement

"StudyBlue is great for studying. I love the study guides, flashcards and quizzes. So extremely helpful for all of my classes!"

Alice , Arizona State University"I'm a student using StudyBlue, and I can 100% say that it helps me so much. Study materials for almost every subject in school are available in StudyBlue. It is so helpful for my education!"

Tim , University of Florida"StudyBlue provides way more features than other studying apps, and thus allows me to learn very quickly! I actually feel much more comfortable taking my exams after I study with this app. It's amazing!"

Jennifer , Rutgers University"I love flashcards but carrying around physical flashcards is cumbersome and simply outdated. StudyBlue is exactly what I was looking for!"

Justin , LSU
StudyBlue is not sponsored or endorsed by any college, university, or instructor.

© 2016 StudyBlue Inc. All rights reserved.

© 2016 StudyBlue Inc. All rights reserved.