MATH 310
Fall 2011
Diﬀerential Equations
Homework Exercises, Set 7
Midterm Exam
on Wednesday, 2 November 2011
Course Information is on
WebCT
Textbook references are to:
Boyce and DiPrima
“
Elementary Diﬀerential Equations and Boundary Value Problems
” (9th edition).
Note:
The
Midterm Exam
is on Wednesday, 2 November, and will include the material covered
in this set of exercises.
Many of the following questions (especially from Section 3.2) are quite short, and are designed to
help you understand and use the theory and results on second-order (and higher-order) equations
from various perspectives.
Reading
:
•
Sections 3.2, 3.4, 4.1, 4.2
Problems to prepare for exam (no need to hand in):
•
Section 3.2,
#
5, 6, 18, 20
The Wronskian
•
Section 3.2,
#
23, 26, 38
Fundamental set of solutions
•
Section 3.2,
#
31, 33, 35, 36
Abel’s Theorem and the Wronskian
•
Section 3.4,
#
6, 9, 14, 18
Repeated real roots of the characteristic equation
•
Section 4.1,
#
6, 9, 16, 19(b,c), 23, 25
Higher-order linear equations; linear independence