dy x
1) Let a 6 y( y _ 2) be the given initial value problem.
y(2) = 1
a) (10 pts.) Using Existence and Uniqueness Theorem show that the initial value
problem has a unique solution.
b) (7 pts. ) Find this unique solution.
c) ( 8 pts.) Determine the interv
MATH 225: DIFFERENTIAL EQUATIONS AND LINEAR
ALGEBRA: Final Exam: May 24, 2006
Final Exam Solutions
1.a) Let A be an n n matrix and k is a (constant) scalar. Show that
the set of all vectors v such that A v = kv is a subspace of Rn . (This means
that eigen
MATH 225: DIFFERENTIAL EQUATIONS AND LINEAR
ALGEBRA
Second Midterm Exam Solutions
1. Prove the following statements: 1.a) Let A be an n n invertible matrix. Then
the homogeneous linear system Ax = 0 has only the trivial solution. Solution: Since
A has inv
MATH 225: DIFFERENTIAL EQUATIONS AND LINEAR
ALGEBRA
Second Midterm Exam
April 25, 2006
17:40 - 19:40
Name
:
ID#
:
Department :
Instructor : Metin Grses
u
The exam consists of 4 questions of equal weight.
Please read the questions carefully.
Show all yo
MATH 225: DIFFERENTIAL EQUATIONS AND LINEAR ALGEBRA
Solutions of First Midterm Exam
March 13, 2006
1.a) Show that the function y (x) = A + Bex + Ce2x satises the dierential
equation y 3y + 2y = 0, where A, B , and C are arbitrary constants.
Solution:
y (x
MATH 225: DIFFERENTIAL EQUATIONS AND LINEAR
ALGEBRA
First Midterm Exam
March 13, 2006
17:40 - 19:40
Name
:
ID#
:
Department :
Instructor : Metin Grses
u
The exam consists of 4 questions of equal weight.
Please read the questions carefully.
Show all you
MATH225 - HW6
Q1
(a) Write a function TransMatrix that takes an n nx1 column vectors (v1 , v2 , .vn ) as input. If these vectors
are linearly independent, compute transition matrix from the standart basis of n to the ordered basis
(v1 , v2 , .vn ). Otherw
BILKENT UNIVERSITY
Mathematics Department
Math225 Dierential Equations & Linear Algebra
Fall Semester 2011-2012
FOURTH HOMEWORK ASSIGNMENT
December 2, 2011
Due Date:
December 12, 2011
Name
:
.
Id. No.
:
.
Section
:
.
IMPORTANT
This homework consists of
MATH 225
2011-2012 Fall
HOMEWORK 2
Due date: October 24, 2011 for Sections 2 and 4,
October 25, 2011 for sections 1and 3.
IMPORTANT:
Homework must be turned in before the first lecture starts. You can turn in your
homework anytime before the deadline. Yo
BILKENT UNIVERSITY
Mathematics Department
Math225 Dierential Equations & Linear Algebra
Fall Semester 2011-2012
FOURTH HOMEWORK ASSIGNMENT
December 2, 2011
Due Date:
December 12, 2011
Name
:
.
Id. No.
:
.
Section
:
.
IMPORTANT
This homework consists of
Q.1
Grading: (a) 10, (b) 4, (c) 6
points
A uniform beam 9.00 m long, weighing
300 N, rests symmetrically on two
supports 5 m apart. A boy weighing
600 N starts at point A and walks
toward the right.
(a) Calculate the upward forces FA and FB exerted on the
4‘
. . m . A. by" ,_ 2 \I
13 COHSIdST the (hi erenual equauon :4 = ~er + 2x x 4. y t X E
at
4 _. , V . . . a. .1 . 2
a) {113 pts,) Solve th1s d1fferent1a1 equatlon by geangjﬁgmegmstaggtmn u = x + y.
M:><Z»er%§ =9
b){ 10 pts.) Verify that the
MATH 225 Linear Algebra and Differential Equations
Fall 2015
Homework 2
Due Date: November 10th, 2015
Name: .
ID Number: .
Department: .
Rules:
1. Include this page in your homework as the cover page. Otherwise, you
will lose 10 points.
2. H
Math 225
Differential Equations & Linear Algebra
Fall Semester 2014-2015
SECOND HOMEWORK ASSIGNMENT
October 23, 2014
Due Date: October 30, 2014
Name : .
Id. No. : .
Section : .
Department :.
IMPORTANT
This homework consists of 5 questions of equal weight.
MATH 225
2013 - 2014 Fall
Lab Assignment #2 Solutions
Q1) a)
dsolve('Dx = x - 1')
ans =
C2*exp(t) + 1
b)
dsolve('Dx = x - 1','x(1) = a')
ans =
(exp(t)*(a - 1)/exp(1) + 1
c)
t = -2 : 0.001 : 1;
a = 2;
x = (exp(t)*(a - 1)/exp(1) + 1;
plot(t,x);
2
1.9
1.8
1.
MATH 225
2013 - 2014 Fall
Lab Assignment #1
Solutions
BASICS
3) The workspace consists of the set of variables built up during a session of using the MATLAB
software and stored in memory. You add variables to the workspace by using functions, running
M-fi
MATH 225
2013 - 2014 Spring
Lab Assignment #1
Due date: March 3, Monday, for all sections.
IMPORTANT
Submit your homework as a hardcopy to your instructor.
Homework must be turned in to your instructor before 5:30 pm of the due date. Late
homework will be
PHYS 101 General Physics-I, Final Exam
Duration: 125 minutes
January 15, 2009
NAME:. Section:.
Q.1 (20)
Q.2 (20)
Q.3 (20)
Q.4 (20)
Q.5 (20)
Total (100)
You must sign the Honor Code for your exam to be graded:
I pledge, on my Honor, not to lie, cheat, or s
Math 225
2009-2010 Fall
Midterm 1 Questions
1) Solve the following initial value problem (4e 2 x + 2 xy y 2 )dx + ( x y ) dy = 0 ,
y(0) = 0.
2
2)Solve the following differential equation
dy x + 2 y 1
.
=
dx 2 x y + 3
3) Find the solution of the following
Bilkent University Department of Mathematics
Math 225 Linear Algebra and Dierential Equations
Fall 2012
Homework 2
Assigned: Monday, 8 October 2012
Due: Monday, 15 October 2012
Name:
Student Number:
Section:
Instructions:
1. Print the homework on 6 A4-siz
Math 225 Fall 2012
Homework 4
due 26 November, Monday
Name
:
ID#
:
Section
:
Print the homework on 6 A4-size sheets. Attach the sheets with a stapler or plastic
sheet protector, but not a paper clip.
Solve the problems on these sheets and their backs if
Bilkent University Department of Mathematics
Math 225 Linear Algebra and Dierential Equations
Fall 2012
Homework 2
Assigned: Monday, 8 October 2012
Due: Monday, 15 October 2012
Name:
Student Number:
Section:
Instructions:
1. Print the homework on 6 A4-siz
MATH 225
HOMEWORK 1
MATLAB ASSIGNMENT 1
Due date: October 8, 2012
Submit your homework as a hardcopy to your instructor.
Homework must be turned in to your instructor before 5:30 pm of the due
date. Late homework will be accepted no later than 5:30 pm o