Variation of Parameters
Solve: y + P( x) y + Q( x) y = f ( x)
Find the complementary function:
yc = c1 y1 + c2 y2
Then find a particular solution of the
form: y p = u1 ( x) y1 + u2 ( x) y2
where
W1
W2
u1 ' =
and u2 ' =
W
W
y1
with W =
y1 '
0
W1 =
f ( x)
y
Differential Equations Section 5.1 Homework: 1, 3, 5, 11, 21, 23, 29
Hookes Law -
F = ks , k = spring constant, s = amount of elongation, F =restoring force
Newtons Second Law Free Undamped Motion or Simple Harmonic Motion
d 2x
+ 2 x = 0 where 2 = k / m ,
Differential Equations Quiz #4
4.5 4.9 Fall 2010 Name
Show all your work neatly on notebook paper. Please circle your answers.
1. Solve: xzy+2xy'6y=0
2. Solve 2 of these 3 problems. It is your choice which two you pick and you may use the method of
Differential Equations Quiz #4
4.5 4.9 Fall 2010 Name
Show all your work neatly on notebook paper. Please circle your answers.
1. Solve: xzy+2xy'6y=0
2. Solve 2 of these 3 problems. It is your choice which two you pick and you may use the method of
Differential Equations
Prerequisite Review
Evaluate the following integrals
x
2 dx
e
1.
2.
3.
x
2
ln xdx
4.
x
3
cos xdx
5.
x e
6.
arctan xdx
7.
x
8.
dx
9.
1 + sin x
dx
cos x
4 2x
dx
dx
2
9 x2
dx
4x2 + 1
x2 9
dx
x
x2 1
10.
x
11.
2 x 3 4 x 2 15 x + 5
x 2
Differential Equations Section 5.2 Homework: 1, 3, 5, 9, 13, 17
First we will solve the boundary-value problem
eigenfunctions. is called a parameter.
y + y = 0,
y (0) = 0,
y ( L) = 0 , using eigenvalues and
Case 1:
= 0 . The general form of the solution
Logistic Model Example Section 3.2
The logistic model: P (t ) =
where
P0 K
P0 + ( K P0 )e r t
(Note that I have written it differently than your text.)
K = carrying capacity of the environment or the saturation level
P0 = initial population
r = rate of gr
Differential Equations Formula Sheet
( x) = e
M y Nx
N
dx
( y) = e
N x M y
M
dT
= k ( T Tm )
dt
dy
P (t ) =
P0 K
P0 + ( K P0 ) e r t
d 2x
+ 2 x = 0 , 2 = k / m , x(t ) = c1 cos t + c 2 sin t , T = 2 / , f = 1 / T = / 2
dt 2
x(t ) = c1 cos t + c 2 sin t
Differential Equations Exam # 3
Spring 2004
Name _
Show all your work neatly and in numerical order on notebook paper. Solutions without correct supporting
work will not be accepted.
1. Use the definition of the Laplace transform to find
Lcfw_ f (t ) for
Differential Equations Exam #3
Fall 2003
Name _
Show all your work neatly and in numerical order on notebook paper. You must omit one problem by clearly writing
OMIT by the problem on your notebook paper. If you do not omit a problem, I will omit the last
Differential Equations Exam #2
Spring 2004
Name_
Show all your work neatly and in numerical order on notebook paper.
DO NOT WRITE ON THE BACKS OF YOUR PAGES.
y c = c1e 2 x + c 2 e 3 x is the complementary function for y y 6 y = g ( x) , write the form of
Differential Equations Exam #2
Fall 2003
Name_
Show all your work neatly and in numerical order on notebook paper. You must omit one problem by clearly writing
OMIT by the problem on your notebook paper. If you do not omit a problem, I will omit the last
Differential Equations Exam #1
Spring 2004
Name _
You must show all your work neatly and in numerical order on the paper provided. Solutions without correct supporting
work will not be accepted. Please do not write on the backs of your pages. Unless indic
Differential Equations Exam #1
September 18, 2003
Name _
Show all your work neatly and in numerical order on notebook paper.
DO NOT WRITE ON THE BACKS OF YOUR PAGES.
1. Given x + x = 0 : (a) Show that
x = c1 cos t + c 2 sin t is a two-parameter family of
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_
_
_
Euler's Method
_
_
Section 2.7
_
1
_
Recall
_
_
As long as the coefficients of our 1st order
differential equation are continuous with
continuous partial derivatives with respect to y, it
has a unique solution surrounding the initial
point.
It i
Differential Equations worksheet, Chapter 1
Determine the order of the given differential equation; also state whether the equation is linear or nonlinear.
1. 1 t y ' '4ty '+5 y = cos t
(
)
2.
t 3 y (4 ) t 2 y ' '+4ty '3 y = 0
3.
yy '+2 y = 1 + t 2
Verify
NorthWest Arkansas Community College
Division of Science and Mathematics
Course: Math 2914, Differential Equations
Credit Hours: 4 credit hours for transfer
Instructor:
Pamela Duck
e-mail: pduck@nwacc.edu
Office Hours:
Fall 2010
_ Syllabus
Prerequisite: M