Willis Thai
MA2132 Worksheet 3
1. Find the solution of the IVP y - 2 y + 5 y = 0 , y (0) = 1 , y (0) = 1 .
r 2 - 2r + 5 = 0 - b b 2 - 4ac 2 - 16 = = 1 2i 2a 2 r = i =1 =2 r= y = C1et cos( t ) + C 2 e t sin( t ) y = C1e t cos(2t ) + C 2
Polytechnic Institute of NYU MA 2132 Worksheet 5
Print Name: Signature: ID #: Instructor: Jacobovits
Date:
Problem 1 2 3 4 5 6 Total
Possible 15 15 15 20 20 15 100
Points
Your signature: (1) Find a fundamental set of solutions for the problem x = Ax where
Polytechnic Institute of NYU MA 2132
Print Name: Signature: ID #: Instructor/Section: Directions: Show all your work for each problem. Problem Possible 1 2 3 4 5 Total 20 20 20 20 20 100 Points
Worksheet 6
Your signature: (1) Use Eulers method to solve y
Polytechnic Institute of NYU
MA 2132
Final Practice Answers
Fall 2012
Studying from past or sample exams is NOT recommended. If you do, it should be only AFTER
you know how to do all of the homework and worksheet problems. These are additional practice
pr
Polytechnic Institute of NYU
MA 2132
Final Practice
Fall 2012
Studying from past or sample exams is NOT recommended. If you do, it should be only AFTER
you know how to do all of the homework and worksheet problems. These are additional practice
problems d
A BRIEF GUIDE TO USING MATLAB IN MA2132
It is strongly recommended that you start using MATLAB as soon as you can. Not only
because MATLAB assignments are part of your grade, but also as a tool to check your
worksheet and practice homework solutions.
The
Polytechnic Institute of NYU
MA 2132
Midterm Practice Answers
Fall 2011B
Studying from past or sample exams is NOT recommended. If you do, it should be only AFTER
you know how to do all of the homework and worksheet problems. These are additional practice
Polytechnic Institute of NYU MA 2132 Worksheet 4
Print Name: Signature: ID #: Instructor: Jacobovits
Date:
Problem 1 2 3 4 5 Total
Possible 16 30 30 12 12 100
Points
Your signature: (1) Rewrite the dierential equation as a rst order system. (a) x tx + x2
Polytechnic Institute of NYU MA 2132 Worksheet 3 NOT COLLECTED
(1) Find the solution of the dierential equation. (a) 3xy + 2y = 0 1 Answer: y = C1 + C2 x 3
(b) 4x2 y y = 0 1 1 Answer: y = C1 x 2 + C2 x 2
(c) x2 y + 4xy + 2y = 0, y (1) = 1, y (1) = 2 Answe
Willis Thai
MA2132 Worksheet 2
1) Construct a slope field for the differential equation y = x + y for - 5 x 5 , - 5 y 5 . Sketch the solution curve corresponding to the initial condition y (0) = 0 , then find y (-4) for this solution.
-5 -10
Willis Thai
MA2132 Worksheet 1
1. Substitute y ( x) = e rx into 3 y + 3 y - 4 y = 0 and determine all values of the constant
r for which y ( x) = e rx is a solution. y ( x) = e rx
y ( x) = re rx y ( x) = r 2 e rx 3r 2 e rx + 3re rx - 4e rx = 0
Willis Thai
MA2132 Worksheet 5
2 2 - 4 1. Find a fundamental set of solutions to x = Ax , where A = 2 - 1 - 2 . 4 2 - 6 dx = x = Ax + f (t ) , 2. (a) Find the general solution to the nonhomogeneous system dt e -t 1 2 where A = 2 1
Willis Thai
MA2132 Worksheet 4
1. Use the method of undetermined coefficients to solve each of the following: a. y + y = cos( x) + 2 x , y (0) = 1 , y (0) = -1 . y + y = 0
r2 +1 = 0 r = 0i y h = C1 cos( x) + C 2 sin( x) y p = Ax sin( x) + Bx cos
Polytechnic Institute of NYU MA 2132 Final Practice Fall 2008B
Studying from past or sample exams is NOT recommended. If you do, it should be only AFTER you know how to do all of the homework and worksheet problems. These are additional practice problems
Polytechnic Institute of NYU MA 2132 Final Practice Answers Fall 2008B
Studying from past or sample exams is NOT recommended. If you do, it should be only AFTER you know how to do all of the homework and worksheet problems. These are additional practice p
Polytechnic Institute of NYU MA 2132 Worksheet 1
Print Name: Signature: ID #: Instructor: Jacobovits
Date:
Problem 1 2 3 4 5 6 Total
Possible 12 16 16 20 16 20 100
Points
Your signature: (1) Consider the dierential equation dy + y ] = x 10. dx (a) Given t
Polytechnic Institute of NYU MA 2132 Worksheet 2
Print Name: Signature: ID #: Instructor: Jacobovits
Date:
Problem 1 2 3 4 5 6 7 8 Total
Possible 10 8 10 10 24 16 14 8 100
Points
Your signature: (1) Find the particular solution of the dierential equation
Polytechnic Institute of NYU
MA 2132
Midterm Practice
Fall 2011B
Studying from past or sample exams is NOT recommended. If you do, it should be only AFTER
you know how to do all of the homework and worksheet problems. These are additional practice
problem