## Exam Information

Login / Sign Up to View Document

## Sample Document Text

Math 211
Final Exam - Answers
Spring 2001
1. Consider the differential equation
y
primeprime
+ 5y
prime
+ 4y = 0.
a) (4 points) Find a fundamental set of solutions.
Answer: The characteristic polynomial is p(?) = ?
2
+5?+4 = (?+1)(?+4). The characterisitic
roots are ?1 and ?4, so the functions
y
1
(t) = e
?t
and y
2
(t) = e
?4t
form a fundamental set of solutions.
b) (3 points) What is the general solution?
Answer: The general solution is
y(t)= C
1
y
1
(t)+C
2
y
2
(t) = C
1
e
?t
+C
2
e
?4t
.
c) (3 points) Find the solution satisfying y(0) = 1 and y
prime
(0) = 2.
Answer: We need to find C
1
and C
2
so that
1 = y(0) = C
1
+C
2
2 = y
prime
(0) =?C
1
? 4C
2
These equations are solved by C
1
= 2 and C
2
=?1. The solution is
y(t)= 2e
?t
?e
?4t
.
2. Consider the differential equation
x
prime
= (1 +x
2
) cos t.
a) (4 points) What is the general solution?
Answer: The equation is separable. Separating variables and then integrating we get
in...

## Related Documents

The Independent Exam

Homogeneous Notes

Substituting Exam

Substituting Exam

The Independent Notes

The Independent Exam

Previous Equation Notes

Either...or Exam

Coefficient Matrix Exam

Eigenvalues Notes

Exact Linear Exam

Eigenvalues Exam

Upper Right-Hand Box Exam

Homogeneous Problem Exam

Nonlinear System Exam

Either...or Notes

© Copyright 2019 , Koofers, Inc. All rights reserved.

The information provided on this site is protected by U.S. and International copyright law, and other applicable intellectual property laws, including laws covering data access and data compilations. This information is provided exclusively for the personal and academic use of students, instructors and other university personnel. Use of this information for any commercial purpose, or by any commercial entity, is expressly prohibited. This information may not, under any circumstances, be copied, modified, reused, or incorporated into any derivative works or compilations, without the prior written approval of Koofers, Inc.