MATH 348 - Fall 2015
Homework Set I
Page numbers refer to the text: Partial Differential Equations and Boundary value
Problems, Nakhlé Asmar(NA).
References Texts: The cited reference sections are from Advanced Engineering
Mathematics by Zill and Cullen, 3rd edition (ZC) and Fundamentals of Differential
Equations, by Nagle, Saff and Snider (NSS) are noted by the boldface initials.
Section
Problems
NA
A.1
3,7,15,17,21,23 ,27
A.2
3,5,9,13
A.3
3,9,11,15,43
Pages
Sections
ZC
NSS
514-15 3.1 2.3 & 4.2
523
3.3
4.6
530-31
3.6
4.7
Topic
1st and 2nd
order problems.
2nd order
problems.
2nd order
problems.
Hand In the Following Problems.
1. (4 points) #24, page 515. Look carefully at (5) with n = 2 on page 511.
2. (4 points) Solve y 00 (x) − y(x) = 0. Compare your solution to #9, page 523.
dy
dy dt
dt dy
1 dy
=
=
=
dx
dt dx
dx dt
x dt
d2 y
and apply this result and the product rule to find 2 .
dx
3. (6 points) #43, page 530. Hint If t = ln(x) then
1
and y2 (x) = x5
x
are solutions to x2 y 00 (x) − 3xy 0 (x) − 5y(x) = 0 on the interval [1, 2]. Let y0 and
y1 be arbitrary fixed numbers and set yg (x) = c1 y1 (x) + c2 y2 (x).
4. (6 points) It is straightforward to check that each of y1 (x) =
(a) (2 points) Show that there is a unique choice of c1 and c2 so that yg (1) = y1
and yg0 (1) = y1 .
(b) (4 points) More generally, let x0 ∈ (1, 2) be arbitrary and show that there
is a unique choice of c1 and c2 so that yg (x0 ) = y1 and yg0 (x0 ) = y1 .