Matthew Dehlinger
Assignment HW s2 1 due 01/30/2015 at 06:00pm CST
spr15rbyerlym3350sD01
y = y(2 y)(4 y)
1. (1 pt)
Find the DISTINCT critical points and classify each as (1) AS
for Asymptotically Stable, (2) US for Unstable or (3) SS for
Semi-Stable.
Cons
Math 3350 Spring 2009, Sample Test # 1, Name 1. Separable Solve the initial value problem y = ex-y with y(1) = 1. Find an explicit solution. ANSWER: y=x x x2 + 1 2. Separable Find the general solution of y = . Find an explicit solution. cos(y) ANSWER: y =
Matthew Dehlinger
Assignment HW s2 3 due 02/05/2015 at 04:00pm CST
spr15rbyerlym3350sD01
y=
.
1. (1 pt)
A rst order linear equation in the form y + p(x)y = f (x) can be
solved by nding an integrating factor (x) = exp
4. (1 pt)
p(x) dx
A rst order linear e
Matthew Dehlinger
Assignment HW s2 3 due 02/09/2015 at 09:00pm CST
spr15rbyerlym3350sD01
(1) Given the equation y + 2xy = 4x nd (x) =
1. (1 pt)
(2) Then nd an explicit general solution with arbitrary constant
C.
A rst order linear equation in the form y +
Matthew Dehlinger
Assignment HW s1 2 due 01/22/2015 at 05:00pm CST
spr15rbyerlym3350sD01
2) Since the function f (x, y) is ? at the point (0, 0), the parf
tial derivative
? and is ? at and near the point (0, 0), the
y
solution to y = f (x, y) ? near the p
Matthew Dehlinger
Assignment HW s2 4 due 02/09/2015 at 05:00pm CST
spr15rbyerlym3350sD01
In this problem we consider an equation in differential form
M dx + N dy = 0.
1. (1 pt)
In this problem we consider an equation in differential form
M dx + N dy = 0.
Matthew Dehlinger
Assignment HW s2 5 due 02/24/2015 at 04:00pm CST
spr15rbyerlym3350sD01
= C.
ln(x)
1. (1 pt)
Transforming u = y/x back into the variables x and y and using
the initial condition y(1) = 3 we nd
Write the equation in the form y = f (y/x) th
Matthew Dehlinger
Assignment HW s2 2 due 02/03/2015 at 04:00pm CST
spr15rbyerlym3350sD01
The general solution can be written as y =
+C
1. (1 pt)
Find an explicit solution of the initial value problem y(0) = 4
Find an explicit general solution for
1) y =
8
Matthew Dehlinger
Assignment HW s3 2 due 03/05/2015 at 04:00pm CST
spr15rbyerlym3350sD01
Finally, after making a selection of a value for C as described
above (you have to choose some nonzero numerical value)
we arrive at
1. (1 pt)
y2 (x) =
So the general
Matthew Dehlinger
Assignment HW s1 1 due 01/22/2015 at 05:00pm CST
spr15rbyerlym3350sD01
1. (1 pt)
(1) (1 x)y 4xy + 5y = cos(x) is a ? ? differential equation with order
.
dy
d3y
dx3
dx
der
.
4
(2) x
= 0 is a ? ? differential equation with or-
2. (1 pt)
2
Matthew Dehlinger
Assignment HW s2 1 due 01/29/2015 at 06:00pm CST
spr15rbyerlym3350sD01
Enter your answer as a comma separated list of pairs consisting
on a critical point and its stability type (e.g. your answer might
look like (2,AS), (-3,SS), (7,US) )
Matthew Dehlinger
Assignment HW s3 1 due 03/03/2015 at 04:00pm CST
spr15rbyerlym3350sD01
on I then the IVP has a unique solution for the point x0 I that
exists on the whole interval I.
1. (1 pt)
Fundamental Existence Theorem
for Linear Differential Equati
April 8, 2015 Test III Math 3350D01
NameiAnguK/fg Uan ZED
In all problems, to receive full credit, give work or state your reasoning clearly. If there is not
sufcient room to work on the test, attach your own paper.
I, Del/m 0( (print name) certify that
April 8, 2015
Test III
Math 3350-D01
Name:
In all problems, to receive full credit, give work or state your reasoning clearly. If there is not
sucient room to work on the test, attach your own paper.
I,
(print name) certify that I have completed all work
Matthew Dehlinger
Assignment HW s3 3 due 03/28/2015 at 11:59pm CDT
spr15rbyerlym3350sD01
4) Given the initial conditions y(0) = 4 and y (0) = 18 nd the
unique solution to the IVP
1. (1 pt)
For a homogeneous constant coefcient linear differential equation
Matthew Dehlinger
Assignment HW s3 4 due 03/28/2015 at 11:59pm CDT
spr15rbyerlym3350sD01
First we consider
y 8y + 16y = 0 :
1. (1 pt)
We consider the non-homogeneous problem y y = x2
the
homogeneous
1) the auxiliary equation is ar2 + br + c =
problem
= 0.
Matthew Dehlinger
Assignment HW s3 2 due 03/06/2015 at 11:59pm CST
spr15rbyerlym3350sD01
Finally, after making a selection of a value for C as described
above (you have to choose some nonzero numerical value)
we arrive at
1. (1 pt)
y2 (x) = Cy1 u =
So the
Matthew Dehlinger
Assignment HW s3 1 due 03/03/2015 at 11:59pm CST
spr15rbyerlym3350sD01
If the coefcients an (x), . . . , a0 (x) and the right hand side of the
equation g(x) are continuous on an interval I and if an (x) = 0
on I then the IVP has a unique
Matthew Dehlinger
Assignment HW s2 5 due 03/03/2015 at 11:59pm CST
spr15rbyerlym3350sD01
where g(u) =
.
1. (1 pt)
An implicit general solution with dependent variable u can be
written in the form
Write the equation in the form y = f (y/x) then use the sub
Matthew Dehlinger
Assignment HW s2 4 due 02/11/2015 at 05:00pm CST
spr15rbyerlym3350sD01
1. (1 pt)
Correct Answers:
In this problem we consider an equation in differential form
M dx + N dy = 0.
4
4
8*x2/2+4*x*y+2*y2/2
(2x + 4y)dx (4x + 3y)dy = 0
3. (1
Matthew Dehlinger
Assignment HW s2 2 due 02/03/2015 at 04:00pm CST
spr15rbyerlym3350sD01
4. (1 pt)
1. (1 pt)
Find an explicit general solution for
1) y =
8
y=
x
Consider the rst order separable equation y =
+C
=C
An implicit general solution can be writt
Matthew Dehlinger
Assignment HW s1 2 due 01/22/2015 at 05:00pm CST
spr15rbyerlym3350sD01
1. (1 pt)
3. (1 pt)
Consider the initial value problem 2xy = 4y, y(1) = 2.
Put the differential equation 5xy + ex y =
y
x2 + 25
into the
form y + p(x)y = g(x) and nd
Matthew Dehlinger
Assignment HW s1 1 due 01/22/2015 at 05:00pm CST
spr15rbyerlym3350sD01
A. y = e3x
1. (1 pt)
B. y = sin(3x) or y = 3 sin(x)
(1) (1 x)y 4xy + 5y = cos(x) is a ? ? differential equa.
tion with order
d3y
dy
dx3
dx
.
der
4
E. y = 3 sin(x)
2 z