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Math 315-2
WHO
Exam 3 Name, ID: Pew“ (9f 7
Show work on every problem. 'Numbers in'the [ ] give the point value for each problem.
1. [10 each] Find the general solution to each ODE:
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a) y(4)+y”——12y=0 ﬂaps-46“
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Math 315-01
Exam 1
Spring 2013
Name:
ID:
Date:
Directions: Show all work. No work equals no credit. You may use a basic scientic calculator, but no graphing/symbolic/cell phone calculators. Use proper
notation.
(4 pts) 1. For the following equations, dete
Math 315-01
Exam 2
Spring 2008
Name:
ID:
Date:
Directions: Show all work. No work equals no credit. You may use a basic
scientic calculator, but no graphing/symbolic calculators. Use proper notation.
(12 pts) 1. Find the solution of the initial value prob
Math 315-01
Exam 1
Spring 2010
Name:
ID:
Date:
Directions: Show all work. No work equals no credit. You may use a basic scientic calculator, but no graphing/symbolic/cell phone calculators. Use proper
notation.
(9 pts) 1. For the following equations, dete
Math 315-01
Exam 1
Spring 2009
Name:
ID:
Date:
Directions: Show all work. No work equals no credit. You may use a basic scientic calculator, but no graphing/symbolic/cell phone calculators. Use proper
notation.
(16 pts) 1. A body of mass m is projected ve
Math 315-01
Exam 1
Spring 2009
Name:
ID:
Date:
Directions: Show all work. No work equals no credit. You may use a basic scientic calculator, but no graphing/symbolic/cell phone calculators. Use proper
notation.
(12 pts) 1. For the following equations, det
Math 315-01
Exam 2
Spring 2009
Name:
ID:
Date:
Directions: Show all work. No work equals no credit. You may use a basic scientic calculator, but no graphing/symbolic/cell phone calculators. Use proper
notation.
(8 pts) 1. Solve the initial value problem y
Math 315-01
Exam 1
Spring 2008
Name:
ID:
Date:
Directions: Show all work. No work equals no credit. You may use a basic
scientic calculator, but no graphing calculators. Use proper notation.
(6 pts) 1. Give an example of a dierential equation of the form
Math 315-1 Exam 2 Review Sheet
Exam number two covers sections 3.1-3.4, 3.6, 4.1, 4.2, and 10.1 No notes and no graphing,
symbolic, cell phone calculators allowed. You may bring a simple scientic calculator, but
most likely you will not need it. Dont be l
This example is a second order differential equation. It is a damped harmonic oscillator
where is the position of the object at time ,
is its mass,
is the spring
constant and
is the damping constant. The initial displacement is 1 with no velocity. D(x)(0)
Math 315-01
Additional Application Problems
Spring 2012
Name:
ID:
Date:
Directions: Show all work. No work equals no credit. Use proper notation.
1. A body of mass m is projected vertically upward with an initial velocity v0 in a medium
oering a resistanc
Math 315-1 Exam 1 Review Sheet
Exam number one covers sections 1.1 to 1.3 and 2.1 to 2.5. No notes and no graphing,
symbolic, cell phone calculators allowed. You may bring a simple scientic calculator, but
most likely you will not need it. Dont be late. B
Math 315-01
Exam 1
Summer 2006
Name:
ID:
Date:
Directions: Show all work. No work equals no credit. You may use a basic
scientic calculator, but no graphing/symbolic calculators. Use proper notation.
(8 pts) 1. Give an example of a dierential equation of
Math 315-2 Exam 3 Name, ID: (51/ I
Show work on every problem. Numloers in the [ ] give the point value for each problem.
1. [10 each] Find the general solution to each ODE:
a) y(4)—2y”—8y=0 b) y”’+8y=3e_t 7p: 456
\ v1: ' - *6
J 9'6 ‘ (3+8 ‘0 Lﬁﬂjééa +34)
Math~315-2 EXAM 1 - ' spring 2014
Name: 2 6M4 (*8 I’D-#2 I _ Signature:
SHOW APPROPRIATE WORK or EXPLANATION on problems 1 and 2 for full credit. Work is optional on #3. .- >
Box or circle your'ﬁnal answers. Numbers in the [ ] indicate what each problem i
p mix '4
Math 315—2 EXAM l ' spring 2014
Name: ID#: I Signature:
SHOW APPROPRIATE WORK or EXPLANATION on problems 1 and for full credit. Work is optional on #3.
Box or circle your ﬁnalanswers. Numbers in the [ ] indicate what each problem is worth. All so
EXAM 1.
Signature:
SHOW APPROPRIATE WORK or EXPLANATION on each problem for full credit. Box or circle your ﬁnal
Math.
Name: Mile. 741W lg? ID#:'
answers.» Numbers in the [ ] indicate what each problem is worth. You’ve been given some info on the last pag
(‘ Vow?
Math 315-2 ' EXAM 1 _ spring 2014
Name: ﬂaw _ ID#: Signaturei '
SHOW APPROPRIAT WORK or EXPLANATION on problems 1 and 2 for full credit. Work is optional on #3.
Box or circle your ﬁnal answers. Numbers in the indicate what each problem is worth. A
EXAM 1 spring 2014
Math 31@
/
Name: I WY? 74V“ ‘2’ ID#
SHOW APPROPRIATE ORK or EXPLANATION on each problem for full credit. Box or circle your ﬁnal
indicate What each problem is worth. You’ve been given some info on the last page.
Signature:
answers.
Math 315-01
Exam 2
Summer 2012
Name:
ID:
Date:
Directions: Show all work. No work equals no credit. You may use a basic scientic calculator, but no graphing/symbolic/cell phone calculators. Use proper
notation. Please show ID before you leave.
(8 pts) 1.
Estimating when a function is within a tolerance.
Here we use Maple to estimate when a function is within a given tolerance level. Let us look at section
3.3 problem number 24. Its analytic solution is
.
What is the smallest value T so is the solution alw
Maple and Series Solutions
This is an example of using Maple to plot various partial sums of a series solution to a DE. First define
the two independent solutions.
(1)
(2)
Now form the particular solution given initial values.
(3)
Now plot various partial
Math 315-01
Final Exam
Spring 2012
Name:
ID:
Date:
Directions: Show all work. No work equals no credit. You may use a basic scientic calculator, but no graphing/symbolic/cell phone calculators. Use proper
notation.
(10 pts) 1. Find the general solution to
Math 315-01
Separation of Variables
Spring 2012
Name:
ID:
Date:
Directions: Show all work. No work equals no credit. Use proper notation.
( ) 1. Assume a solution of the linear homogeneous partial dierential equation having the
separation of variables for