FINAL EXAM
Fall 267
Circle the correct answer. If you circle more than one answer the
credit for a problem is zero.
Problem 1.(10 POINTS.)Solution y (x) to the initial value problem
(x + 2xy )
dy
= (x2 + y 2 + y ),
dx
y (1) = 1
satises the equation:
x3
7
Elementary Differential Equations and Laplace Transforms.
MATH 267

Spring 2014
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Elementary Differential Equations and Laplace Transforms.
MATH 267

Spring 2014
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Elementary Differential Equations and Laplace Transforms.
MATH 267

Spring 2014
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Elementary Differential Equations and Laplace Transforms.
MATH 267

Spring 2014
MATH 267 Test N0. 3 SPRING 2016, Sections 1419, 2628
Problem 1(20 Points)
Calculate the Laplace Transform of the function f = f (t) Which is equal to
e3t when t is 1 _<_ t < 2 and equal to O for any other value of t.
Problem 2(20 points)
Calculate the inv
Elementary Differential Equations and Laplace Transforms.
MATH 267

Spring 2014
Math 267 DifferentialEquations
Exam 2 Review
The following is a list of example problems from each section that will be covered in the second exam. In
order to fully use this review sheet, you should attempt all problems on your own. You should consult th
Elementary Differential Equations and Laplace Transforms.
MATH 267

Spring 2014
Math 267 DifferentialEquations
Exam 2 Review
The following is a list of example problems from each section that will be covered in the second exam. In
order to fully use this review sheet, you should attempt all problems on your own. You should consult th
Elementary Differential Equations and Laplace Transforms.
MATH 267

Spring 2014
MATH 267 Test No. 3 SPRING 2016, Sections 1419, 2628
Problem 1(20 Points)
Calculate the Laplace Transform of the function f = f (t) which is equal to
e3t when t is 1 t < 2 and equal to 0 for any other value of t.
Problem 2(20 points)
Calculate the inver
Elementary Differential Equations and Laplace Transforms.
MATH 267

Spring 2014
Table of Lapiace Transforms
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Elementary Differential Equations and Laplace Transforms.
MATH 267

Spring 2014
lK/llsrlt: 26? Practice rfest Not, 3 SPRENG 2&6 Eectloas lllw'lg 26m28
Problem. M20 P013)
Calculate the Laplace Transform of the function f : f(t) which is equal to t2
when 0 g t < l and equal to 17 when t Z 1.
Problem 2(20 points)
Calculate the inverse t
Elementary Differential Equations and Laplace Transforms.
MATH 267

Spring 2014
MATH 267 (Sections 1419 and 2628) Test No. 1 SPRING 2016
Problem 1 (25 points)
Find the general solution in explicit form of the following differential equation
dy
= 2(y 2 1)x
dx
and the solution corresponding to the initial condition y(0) = 20.
Problem
Elementary Differential Equations and Laplace Transforms.
MATH 267

Spring 2014
MATH 267
Spring 2016
FINAL EXAM
Show your work!
Do not write on this test page except your name and section number
1. (12 points) Find the general solution of the differential equation
y2 + 4
y =
x2
0
2. (12 points) Find the solution of the following Init
Elementary Differential Equations and Laplace Transforms.
MATH 267

Spring 2014
MATH 267 Test No. 2 SPRING 2016, Sections 1419, 2628
Problem 1(35 Points)
Find the general solution of the system
d
~x = A~x,
dt
where A is the matrix
A=
0
0
2 4
1 3
Is the point
a stable or an unstable equilibrium point for the given
system? Why?
Pro
Elementary Differential Equations and Laplace Transforms.
MATH 267

Spring 2014
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Elementary Differential Equations and Laplace Transforms.
MATH 267

Fall 2013
4.4: Nonhomogeneous Equations: The Method of Undetermined Coefficients
4. Rewriting the righthand side in the form 3t = e(ln 3)t = ert, where r = ln 3, we
conclude that the method of undetermined coefficients can be applied.
10. yp(t) 3 is a particular s
Elementary Differential Equations and Laplace Transforms.
MATH 267

Winter 2016
To P 1
MATH 267 Fall 2014 FINAL EXAM
Show your work and explain your answers; Circle your ﬁnal answer
1. (a) (10 points) Find the general solution of the differential equation
(b) (10 points) Find the solution of the initial value problem
y' = xeyV$2
Elementary Differential Equations and Laplace Transforms.
MATH 267

Winter 2016
Math 1357 N &n‘1€5:
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Elementary Differential Equations and Laplace Transforms.
MATH 267

Winter 2016
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MATH 267 I Fall 2014 FINAL EXAM Make—UP
Show your work and explain your answe
Elementary Differential Equations and Laplace Transforms.
MATH 267

Spring 2016
MATH 267 (Sections 1419 and 2628) Practice Test No. 1 SPRING
2016
Problem 1 (25 points)
Find the general solution in explicit form of the equation
1 y xy
dx + exy dy = 0
+ e
x x
and the solution corresponding to the initial condition y(1) = 0.
Problem 2