Docsity
Log inSign up
Docsity
Prepare for your exams
Prepare for your exams

Study with the several resources on Docsity

Earn points to download
Earn points to download

Earn points by helping other students or get them with a premium plan

Guidelines and tips
Guidelines and tips
Sell on Docsity
Sell on Docsity
Log inSign up

Prepare for your exams

Study with the several resources on Docsity

Find documents

Prepare for your exams with the study notes shared by other students like you on Docsity

Search Store documents

The best documents sold by students who completed their studies

Search through all study resources
Docsity AINEW

Summarize your documents, ask them questions, convert them into quizzes and concept maps

Explore questions

Clear up your doubts by reading the answers to questions asked by your fellow students

Earn points to download

Earn points by helping other students or get them with a premium plan

Share documents
download point icon20 Points

For each uploaded document

Answer questions
download point icon5 Points

For each given answer (max 1 per day)

All the ways to get free points
Get points immediately

Choose a premium plan with all the points you need

Study Opportunities

Choose your next study program

Get in touch with the best universities in the world. Search through thousands of universities and official partners

Community

Ask the community

Ask the community for help and clear up your study doubts

University Rankings

Discover the best universities in your country according to Docsity users

Free resources

Our save-the-student-ebooks!

Download our free guides on studying techniques, anxiety management strategies, and thesis advice from Docsity tutors

From our blog

Exams and Study
Go to the blog

Differential Equations Practice Exam 1, Exams of Differential Equations

Brigham Young University (BYU)Differential Equations

20 Unsolved Questions for Practice Exam 1.

Typology: Exams

2018/2019

Uploaded on 02/11/2022

christina
christina 🇺🇸

4.6

(23)

404 documents

1 / 7

Toggle sidebar

This page cannot be seen from the preview

Don't miss anything!

bg1
Name:
Student ID:
Section:
Instructor: Webb
Math 334 (Differential Equations)
Practice Exam 1
Instructions:
•For questions which require a written answer, show all your work. Full credit will be given only if
the necessary work is shown justifying your answer.
•Simplify your answers.
•Calculators are not allowed.
•Should you have need for more space than is allocated to answer a question, use the back of the page
the problem is on and indicate this fact.
•Please do not talk about the test with other students until after the last day to take the exam.
pf3
pf4
pf5

Partial preview of the text

Download Differential Equations Practice Exam 1 and more Exams Differential Equations in PDF only on Docsity!

Name: Student ID: Section: Instructor: Webb

Math 334 (Differential Equations)

Practice Exam 1

Instructions:

  • For questions which require a written answer, show all your work. Full credit will be given only if the necessary work is shown justifying your answer.
  • Simplify your answers.
  • Calculators are not allowed.
  • Should you have need for more space than is allocated to answer a question, use the back of the page the problem is on and indicate this fact.
  • Please do not talk about the test with other students until after the last day to take the exam.

Part I: True False Questions: Circle either True or False for each question. (3 points each)

  1. The equation y′^ = sin(x^2 − 1)y y^2 − 1

is separable.

a) True b) False

  1. The initial value problem (4 − t^2 )y′^ + 2ty = 3t^2 , y(1) = −3 has a unique solution in the interval − 2 < t < 2.

a) True b) False

  1. Every solution of the differential equation dy dt

= y − 5 can be written in the form y = 5 + cet^ for some constant c.

a) True b) False

  1. Suppose an object falling through the atmosphere of a certain planet is accelerated by gravity at a rate of 10. 2 m/s^2. If drag acts in the upward direction at a rate proportional to the objects velocity squared then dv dt = − 10. 2 − γv^2

is the rate of change of the objects velocity for some γ > 0.

a) True b) False

  1. Let y′^ = −(1 − y/K) where K > 0. If y(0) > K/2 and y(0) 6 = K then lim t→∞ y(t) = K.

a) True b) False

  1. The equation y = 5 e^3 t^ is a solution of the differential equation 4 y′′^ − 8 y′^ + 3 y = 0.

a) True b) False

Part III: Justify your answer and show all work for full credit.

  1. Find the solution of the initial value problem

dy dx

y^2 x

, y(1) = 2.

State the solution in explicit form.

  1. For the following differential equation, determine (without solving) an interval on which the solution of the equation is certain to exist and be unique. Justify your answer.

(ln t)y′^ + y = cot t; y(1/2) = 2.

  1. Show that the following equation is exact, then find the solution.

(3x^2 − 2 xy + 2) + (6y^2 − x^2 + 3)y′^ = 0

  1. The following differential equation is not exact. Find an integrating factor and solve the given equation. ( (^) y^2 x

2 y +

x

y′^ = 0

  1. Consider a tank used in certain hydrodynamic experiments. After one experiment the tank contains 100L of a dye solution with a concentration of 2 g/L. To prepare for the next experiment, the tank is to be rinsed with fresh water going in at a rate of 3 L/min, the well-stirred mixture going out at the same rate. Find the time that will elapse before the concentration of dye in the tank reaches 5% of its original value.
  2. Let dy/dt = y^2 (y/ 2 − 3)(1 − 2 y). Sketch the equation’s phase line and use this to determine the equations critical (equilibrium) points. Also, classify each point as either asymptotically stable, unstable, or semi-stable and sketch a few approximate solutions in the ty-plane.

END OF EXAM