Fall 2013 Math V3027 ODE
Instructor: Bohan Fang
Practice Midterm 1 75 minutes
Instructions:
You may not consult any outside sources, including but not restricted
to documents, calculators, computers, phones and other students.
This test has 6 problems a
FALL 2013 MATH V3027 ODE, MIDTERM I SOLUTIONS
1. Note that the general solution to the associated homogeneous equation y
y = 0 is c1 et + c2 et . Therefore we need to assume
Y0 = Ctet
as a particular solution. Plugging this Y0 into the equation
2Cet + Ct
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Fall 2013 Math V3027 Ordinary Differential Equations
Instructor: Bohan Fang
Midterm II
1:10 pm2:25 pm, Nov 19, 2013
Instructions:
You may not consult any outside sources, including but not restricted
to documents, calculators, comput
Ordinary Differential Equations Problem Set 8
Oren Weiss
November 7, 2013
Note: Please be clear about the assumptions that you are making. For
example, in problem 4, it is a very important assumption to make that the
solution is valid for t 6= 0 only. Oth
Ordinary Differential Equations Problem Set 7
Oren Weiss
October 24, 2013
1
Boyce 5.6 Problem 5
Solution: The equation is x2 y 00 + 3(sin x)y 0 2y = 0. We have P (x) = 0. So
xp(x) = 3 sinx x and x2 q(x) = 2. Therefore,
lim 3
x0
sin x
= 3,
x
lim 2 = 2
x0
S
PRACTICE FINAL, ODE MATH V3027, 170MIN
1. Please find the general solution to the equation
y 00 2y 0 + y = 0.
2. The following is a second order homogeneous equation
1
y = 0, t > 0.
t2
Let y1 and y2 be two solutions to the equation above, such that
y 00 +
Ordinary Differential Equations Problem Set 3
Solutions
Oren Weiss
September 26, 2013
Note: I do need some work on these questions (for example, section 4.4
Problem 15) in order to give yall full credit.
1
Boyce 3.3 Problem 7
Solution: The equation is y 0
Ordinary Differential Equations Problem Set 6
Oren Weiss
October 24, 2013
1
Boyce 5.4 Problem 11
Solution: The equation, x2 y 00 + 2xy 0 + 4y = 0, clearly has a singular point at
x = 0. We assume that y = xr is a solution to this equation. Solving gives
(
Ordinary Differential Equations Problem Set 2
Oren S. Weiss
September 19, 2013
Note: Please staple your assignments together if you use more than one
piece of paper. There is a stapler next to the undergraduate math office
(near the math help room). Ill t
PRACTICE FINAL, ODE MATH V3027, 170MIN
1. Please find the general solution to the equation
y 00 2y 0 + y = 0.
y = c1 et + c2 tet .
2. The following is a second order homogeneous equation
1
y 00 + ln(t)y 0 + 2 y = 0, t > 0.
t
Let y1 and y2 be two solutions
x
1. The integrating factor is (x) = ee , and the general solution is
t
y = 3 + Cee , for any constant C.
2. Assume the second solution is y(t) = u(t)t and then plug into the equation
we get
t2 (u00 t + 2u0 ) + 2t(u0 t + u) 2ut = 0,
t3 u00 + 4t2 u0 = 0,
t
Ordinary Differential Equations Problem Set 1
Oren S. Weiss
September 12, 2013
1
Boyce Section 2.1 Problem 16
Solution: Use method of integrating factors: let (t) be the integrating
factor. Multiply both sides by (t) so that we have (t)y)0 = y 0 (t) + 0 y
Spring 2013 Math E1210 Section 1 and 2 ODE
Practice Midterm 2 75 minutes
Instructor: Bohan Fang
Instructions:
You may not consult any outside sources, including but not restricted
to documents, calculators, computers, phones and other students.
This tes
Spring 2013 Math E1210 Section 1 and 2 ODE
Instructor: Bohan Fang
Practice Midterm 1 75 minutes
Instructions:
You may not consult any outside sources, including but not restricted
to documents, calculators, computers, phones and other students.
This tes
Spring 2013 Math E1210 Section 1 and 2 ODE
Practice Midterm 2 75 minutes
Instructor: Bohan Fang
Instructions:
You may not consult any outside sources, including but not restricted
to documents, calculators, computers, phones and other students.
This tes
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Math E1210.002 Ordinary Dierential Equations
Instructor: Bohan Fang
Midterm 1
4:10pm5:25 pm, February 20, 2013
Instructions:
You may not consult any outside sources, including but not restricted
to documents, calculators, computers,
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Math E1210.001 Ordinary Dierential Equations
Instructor: Bohan Fang
Midterm 2
2:40pm3:55 pm, April 3, 2013
Instructions:
You may not consult any outside sources, including but not restricted
to documents, calculators, computers, phon
Spring 2013 Math E1210 Section 1 and 2 ODE
Instructor: Bohan Fang
Practice Final Exam 120 minutes
Instructions:
You may not consult any outside sources, including but not restricted
to documents, calculators, computers, phones and other students.
This t
Spring 2013 Math E1210 Section 1 and 2 ODE
Instructor: Bohan Fang
Practice Midterm 1 75 minutes
Instructions:
You may not consult any outside sources, including but not restricted to
documents, calculators, computers, phones and other students.
This tes
Spring 2013 Math E1210 Section 1 and 2 ODE
Instructor: Bohan Fang
Practice Final Exam 120 minutes
Instructions:
You may not consult any outside sources, including but not restricted
to documents, calculators, computers, phones and other students.
This t