Math 33B: Dierential Equations
Homework 6: Second order ODEs & Applications
Due on: Fri., Nov 21, 2014 -
9:00 AM
Instructor: aliki m.
Please include your name, UID and discussion section on the submitted homework.
Problem 1
In the following problems, sol

Mathematics 33B: Homework 1
Due 4/9.
NOTICE: Only the problems in bold face are to be turned in. The rest of
the problems are suggested problems that you should try hard to solve and
write up. You will not turn in these problems though. My suggestion is t

Mathematics 33B: Homework 5
Due 5/14.
NOTICE: Only the problems in bold face are to be turned in. The rest of
the problems are suggested problems that you should try hard to solve and
write up. You will not turn in these problems though. My suggestion is

Mathematics 33B: Homework 3
Due 1/26.
NOTICE: Only the problems in bold face are to be turned in. The rest of
the problems are suggested problems that you should try hard to solve and
write up. You will not turn in these problems though. My suggestion is

Mathematics 33B: Homework 2
Due 4/16.
NOTICE: Only the problems in bold face are to be turned in. The rest of
the problems are suggested problems that you should try hard to solve and
write up. You will not turn in these problems though. My suggestion is

Mathematics 33B: Homework 6
Due 5/28.
NOTICE: Only the problems in bold face are to be turned in. The rest of
the problems are suggested problems that you should try hard to solve and
write up. You will not turn in these problems though. My suggestion is

Mathematics 33B: Homework 6
Due 5/28.
NOTICE: Only the problems in bold face are to be turned in. The rest of
the problems are suggested problems that you should try hard to solve and
write up. You will not turn in these problems though. My suggestion is

Mathematics 33B - Practice Midterm
NAME (please print legibly):
Your University ID Number:
Your Discussion Section and TA:
Signature:
Calculators, notes and books may not be used in this examination.
You may not receive full credit for a correct answer

Mathematics 33B - Practice Final
Instructor : D. E. Weisbart
NAME (please print legibly):
Your University ID Number:
Your Discussion Section and TA:
Signature:
QUESTION VALUE SCORE
1
20
2
20
3
20
4
20
5
20
6
20
7
20
8
20
9
20
TOTAL
100
1
1. (20 points) An

Mathematics 33B - Practice Final
Instructor : D. E. Weisbart
NAME (please print legibly):
Your University ID Number:
Your Discussion Section and TA:
Signature:
QUESTION VALUE SCORE
1
10
2
10
3
10
4
10
5
10
6
10
7
10
8
10
9
10
10
10
TOTAL
100
1
1. (10 poin

Solutions to Additional Questions
Problem 1. Determine which equilibrium solutions to the equation
dy
dt
= y 3 (1+y)2 (2y)
are asymptotically stable and which are unstable. Then make a rough sketch showing the
behavior of the solutions to this equation.
d

Math 33B: Dierential Equations
Review 11: Reduction of order
Feb. 12, 2014
1
Instructor: aliki m.
Introduction
The reduction of order method is a general method for solving linear, homogeneous ODEs
even when the coecients of y and y are nonconstant functi

Math 33B: Dierential Equations
Practice problems for nal: Section A
June 2013
Instructor: Aliki M
1. Find the particular solution of
x2 y = ey ,
with y(1) = 0.
What is the interval of existence of this solution?
2. Find the general solution y(x) to the fo

Math 33B: Dierential Equations
Midterm Exam 1
Wednesday, Apr. 24, 2013 -9:00 - 9:50 AM
Instructor: Aliki M.
Name:
PLEASE PRINT
UID:
Section:
Discussion sections:
Tuesday with: S. Kim - 1A | F. Robinson - 1C | J. Rooney - 1E
Thursday with: S. Kim - 1B |

Math 33B: Dierential Equations
Midterm Exam 2
Wednesday, May 22, 2013 -9:00 - 9:50 AM
Instructor: Aliki M.
Name:
PLEASE PRINT
UID:
Section:
Discussion sections:
Tuesday with: S. Kim - 1A | F. Robinson - 1C | J. Rooney - 1E
Thursday with: S. Kim - 1B | F

Math 33B: Dierential Equations
Practice problems 1
Instructor: Aliki M.
ANSWERS
Problem 1
y 3 4y x3 + 1 = 0
16
The solution is dened within |x3 1| < .
3 3
Problem 2
x2 + 1
y=
2
The solution is dened for all values of x, i.e. within < x < .
Problem 3
Crit

Math 33B: Dierential Equations
Practice problems 2
Instructor: Aliki M.
ANSWERS
Problem 1
(ii)
(iii)
x
1
yp (x) = x ln x
4
16
x
1
y(x) = c1 x + c2 x3 + x ln x
4
16
Problem 2
y(x) = 2e2x + 6ex
Problem 3
(ii)
y(x) = c1 e2x + c2 ex xex .
(iii)
1
y(x) = c1

Math 33B: Dierential Equations
Practice problems 1: 1st order ODEs
April 2013
Instructor: Aliki M.
Review list
Midterm 1 will focus on solving rst order ODEs using the techniques covered in
Lectures 1-9:
separating variables [Lectures 1 & 2]
integratin

Math 33B: Dierential Equations
Practice problems 2: 2nd order ODEs
May 2013
Instructor: Aliki M.
Review list
Midterm 1 will focus on solving second order ODEs and the material is covered in
Lectures 10-18.
Homogeneous second order ODES:
The second orde