MATH 2930 : HW8 SOLUTIONS
Chapter 4.2 (page 234)
(4.2.29). The characteristic equation is r3 + r = 0. We can factor out an r from this equation to
get r(r2 + 1) = 0. In this form, we see that the roots are r = 0, i
So the general solution is of the form y
HW2 solutions
t
2.1-16 y 0 + 2t = cos
is of the formR y 0 + p(t)y = g(t), so if we multiply the equation by the
t2
2
integrating factor (t) = e t dt = e2 ln |t| = t2 , we have t2 y 0 + 2ty = cos t = (t2 y)0 .
Integrate both sides and we obtain t2 y = sin
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
Due 7/3/14
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Math 1110 Homework 4 Solutions
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1
Problem. Blood ow
When uid ows down a pipe not all the particles travel at the same velocity. In laminar ow,
uid particles move along straight parallel paths in layers, called laminae. The velocity in adjacent
layers are not the same. Those in the cente
1
Problem. Battery
We will insist on the importance of units in engineering applications. Dimensions indicated by
numbers depend on the corresponding units: 1 meter = 100 centimeter, but 1 does not equal 100.
The number and the unit are inseparable, at le
1
Problem. (MAE/TAM) The Shape of a Hanging Cable.
The gure below shows part of a exible cable hanging under its own weight (which is w N/m).
The gure also shows a diagram of the forces which, in equilibrium, must add to zero. A exible
cable is one that c
1
Problem. Derivatives re-visited
In engineering and scientic problems, the data are often noisy: even if the tabulated function
f (x) is supposed to be nice and smooth, errors in measurement and computation might affect
the result. Often the errors in me