Diy Qs Section 5 Problems
Peter Tseng
March 1, 2010
9
We notice that the given equation x2 y 5xy + 9y = 0 (x > 0) ts the form
of the homogeneous second-order linear ODE y + p(x)y + q(x)y = 0 by rst
9
5
dividing by x2 , giving us p(x) = x , q(x) = x2 . As
HW 38 Solutions
May 3, 2013
14.(a) Find the solution of Laplaces equation in the rectangle 0 < x < a
and 0 < y < b that satises the boundary conditions
ux (0, y) = 0, ux (a, y) = 0, 0 < y < b
u(x, 0) = 0, u(x, b) = g(x), 0 x a.
Solution: The general form
MATH 2930 - Spring 2010
Worksheet 9
MATH 2930 - Dierential Equations - Spring 2010
Worksheet 9 - Select Solutions
1. (E&P 8.2, #24)
Use the power series method (i.e., assume solution y(x) =
order ODE
(x2 1)y + 2xy + 2xy = 0
cn xn ) to solve the 2nd-
Apart
MATH 2930 - Spring 2010
Worksheet 10
MATH 2930 - Dierential Equations - Spring 2010
Worksheet 10 - Select Solutions
For each of the following periodic functions f (t) whose value in one complete period is
given, nd its Fourier series.
1. f (t) = t for 0 <
MATH 2930 - Extra Credit 2
Wednesday, February 10, 2010
7:07 PM
3, 5: Courtesy of Anthony Basile
8: Courtesy of George Lu & Pam Snodgrass
Notes Page 1
9, 10, 11, 12: Courtesy of Caroline Chang & Mahina Wang
Notes Page 2
Notes Page 3
MATH 2930 - Extra Credit 3
Tuesday, February 16, 2010
10:49 PM
9, 10: Courtesy of David Smith
11: Courtesy of Jeffrey Hsiao
Notes Page 1
12: Courtesy of Claire Paduano
The bifurcation in this case looks like a pitchfork because when k>0, there are three c
MATH 2930 - Extra Credit 1
Tuesday, February 02, 2010
8:00 PM
3. y'=|y| (Solution provided by Caroline Chang & Mahina Wang, revised by Joe)
Plot of y'=|y|
Plot of y = y2
The slope fields of y = y2 slopes up quicker than the slope fields of y = |y|. As the
MATH 2930 - Extra Credit 4
Monday, February 22, 2010
10:31 AM
3. Courtesy of Claire Paduano
4. Courtesy of Pam Snodgrass & George Lu
Notes Page 1
5. Courtesy of Lee Carlaw
Notes Page 2
Notes Page 3