Emily Czepiel MATH 240 Anna Melikyan 7:30-8:20AM
3. How can you recognize the zeros and poles of the functions from just looking at the colors
you see in the Top View?
One may recognize the zero and p
Recitation Instructor
Name ___________ Recitation Time
Differential Equations MATH 240
Exam 1
February 26, 2002
Show all your work in the space provided under each question. Each problem is worth
NAME # Recitation Instructor ________..._
Signature _____..._ Recitation Time
Elementary Differential Equations
Math 240, Fall 2006
First Examination, September 19, 2006
Show all your work in t
1. Solve the following initial value problem:
dy
1
=
dt
2y + 1
y (0) = 2 .
Separable
Intermediate step:
y 2 + y t 2 = 0.
Final answer after using the quadratic formula:
1 9 + 4t
.
y=
2
2. Find the gen
4 Q i\
Name C Recitation Time
Differential Equations - MATH 240
Exam 1
September 18, 2001
Show all your Work in the space provided under each question. Point values of each
question are indicated
1. Solve the following initial value problem without using the Laplace
transform. (Use substitution.)
x (t) = 2x(t) 2y (t)
y (t) = x(t) + 3y (t)
x(0) = 4
y (0) = 3
10
2
x(t) = et + e4t
3
3
1
10
y (t)
Emily Czepiel
Proposition 1 One can draw a finite line segment between any two different points.
Proposition 2 One can extend a finite line segment as far as we want in a line.
Proposition 3 One can d
While I was in high school, I have always had an interest in serving my country. My brother was
prior enlisted with the Navy. I knew I would either pick between the Navy and the Marine Corps. I wasnt
Emily Czepiel Lab #2
MATH 240
Anna Melikyan
Lab: 7:30-8:20 AM TU
5. Approximate y(2) for each of the initial value problems using Eulers method, first with a
step size of h = 0.10 and then with a step
Emily Czepiel
1. Let y = cos(x) + sin(y). Find a value for y (-4) so that -1 < y (5) < 1.
y (-4) = 0.732
2. Let y = y x/2. Find a value for y (-4) so that -3 < y (5) < 0.
y (-4) = 1.5004
3. Let y = (x
1. Find y(t) by using the Laplace transform. (You dont need to find
x(t).)
x (t) = 3x(t) y(t)
x(0) = 4
y (t) = x(t) + 3y(t)
y(0) = 2
y(t) = 4e3t sin t 2e3t cos t .
2. Find the equilibrium point in the
1. Write down the general solution of each of the following ODEs:
(a) y 11y + 30y = 0.
y(t) = c0 e5t + c1 e6t .
(b) y + 3y + 10y = 0.
32 t
y(t) = c0 e
( )
( )
3
31
31
cos
t + c1 e 2 t sin
t .
2
2
(c)
1. Solve the following initial value problem:
dy
x
= 3y +
dx
y
y(0) = 5 .
Bernoulli.
dy
+ 3y = x y 1 .
dx
The change of variables y = v 1/2 leads to:
dv
+ 2 3v = 2x .
dx
The simplest integrating facto
l. Solve the initial value problem
rcf' + 553 -I- 6:1: = 5(t - 1) a;(0) = 0,a;(0) :1
by using Laplace transforms.
-s
Saga304 +sfsm_o3 mm) 7, e
i. *3
(91%?5+Q)Li)< - 3 +1 \ A A + g
4 6:5 3 @4730) '51?
1. Write down the general solution of each of the following ODEs:
(a) y + 3y + 2y = 0.
(b) y + 4y + 8y = 0.
(c) y 4y + 4y = 0.
(a) y (t) = c1 et + c2 e2t .
(b) y (t) = c1 e2t cos(2t) + c2 e2t sin(2t)
NAME M Recitation Instructor ______.___________
Signature _________ Recitation Time
Elementary Differential EquationsMath 240
Second Examination, October 21, 2008
Show all your work in the space
Name:_
1. Solve the initial value problem y '+ 4 y '+ 3 y = 0 , y(0) = 1, y(0) = 0.
Name:_
2. Solve the initial value problem
dy x 2 2 xy + y 2
=
, y(0) = 2.
dx x 2 2 xy + 3 y 2
Name:_
3. Find the gen