M343 Homework 1
Enrique Areyan
May 10, 2013
Section 1.3
2. Second order, nonlinear.
4. First order, nonlinear.
6. Third order, linear.
13. Given the following second order, linear differential equation: y 00 + y = sec(t), 0 < t < /2, let us check
that the
MATH 343‘ Summer I-2813~ ‘- - v - August- 1-3;}?-
Aseel Farhat
Quiz#1 7 Name: E‘Wﬁ a
You have 20 minutes to ﬁnish the following 3 problems.
1. (5 points) Solve the following I.V.P.
E
t2—
+
(M bTaﬂdav‘cl Emu“; (ﬁdhplq Vlﬂuﬁ T3)
, J v
‘3‘ + 55.
L 7.
more,
MATH .343 Summer. I 20.13. . . . . June 5"” ,2013 .
Aseel Farhat
Quiz#3 Name:
" . (2 flew“
You have 20 minutes to ﬁnish the following 2 problems.
1 . (8 points) Use the method of undetermined coeﬂicients to determine yp for the
following ODES. Don’t sol
MATH 343 Summer I 2013 May 213t ,2013
Aseel Farhat I ' ' ' ' ' ' .
Quiz#2 Name: EOZlQUQ: %T€‘:| 8’0 .
You have 20 minutes to ﬁnish the following 2 problems.
1. (7 points) Verify that the function '91 and y; are solutions of the given O.D.E.
Do they consti
M343 Homework 8
Enrique Areyan
June 10, 2013
Section 5.1
P
1.
(x 3)n . To determine the radius of convergence of this series we apply the ratio test:
n=0
(x 3)n+1
= |x 3| lim 1 = |x 3| 1 < 1 = 1 < x 3 < 1 = 2 < x < 4
lim
n
n
(x 3)n
Hence, if x (2, 4)
M343 Homework 7
Enrique Areyan
June 05, 2013
Section 4.2
16. Consider the equation y (4) 5y 00 + 4y = 0. The solution is given by solving the characteristic equation:
r4 5r2 + 4 = 0
It is not hard to see (or using the rational root theorem) that 1 is a ro
M343 Homework 6
Enrique Areyan
May 31, 2013
Section 3.5
2.
y 00 + 2y 0 + 5y = 3sin(2t).
yg = yh + yp ,
The general solution is given by:
yp is the solution to the associated homogeneous equation and yp is the particular solution
yh : Characteristic equati
M343 Homework 3
Enrique Areyan
May 17, 2013
Section 2.6
3. Consider the equation: (3x2 2xy + 2)dx + (6y 2 x2 + 3)dy = 0. Let M (x, y) = 3x2 2xy + 2 and
N (x, y) = 6y 2 x2 + 3. Since:
M
N
= 2x =
y
x
We can conclude that this is an exact equation. The solut
M343 Homework 5
Enrique Areyan
May 24, 2013
Section 3.4
12. Consider the homogeneous, 2nd O.D.E with constant coefficients: y 00 6y 0 + 9y = 0 and initial conditions:
y(0) = 0, y 0 (0) = 2. The characteristic equation of this O.D.E is (r 3)2 = 0, so we ha
M343 Homework 2
Enrique Areyan
May 15, 2013
Section 2.3
1. Let Q(t) = the amount of dye in grams in the tank at time t. (Time in minutes). We want to find:
dQ
= rate of dye into the tank rate of dye out of the tank
dt
Since we want to clean the tank, the
Indiana University
Department of Mathematics
/
Name: Q‘JC AV 4, Student ID:
Math 343
Midterm
May 28, 2013
You are not allowed to use calculators or any other computational devices. Show all work.
No credit will be given for unsupported answers.
\.
Eith