UCLA Math 33BiEXELHI #17Winter 2015 1
1. (10 points) Find the value of a for which the ODE
9323/ + 3rr2 + (my = 0 (1)
is exact, and then nd the general solution to the equation( )using this value of a
jMeB/Wv(13M/Wir4/WW
OCLJgri-(M 4400291494: 0 , If (1)
NOTES FOR 2/24/15 SECTION 1C
MATT
These are notes on solving systems with a repeated eigenvalue. This is a little trickier, and involves
more linear algebra, than what we have done so far. Hopefully, these notes help clarify the discussion
in section.
1.
ADDITIONAL PRACTICE MIDTERM 2
MATT
I collected some problems that may be helpful for the second midterm. A few are from the book.
Problem 1. Let f (y) = 16y y 3 .
Sketch a graph of f (y).
Find the equilibrium points of the system:
y 0 = f (y).
(1)
Sket
Math 33B: Differential Equations
Practice for final: Answers
Instructor: aliki
Dec. 2014
Problem 1
y(x) = ln(x), 0 < x <
Problem 2
y(x) =
Problem 3
"
x = c1
c
x ln x x
+ 2
3
9 x
cos t
sin t
Problem 4
y(x) =
+ c2
sin t
cos t
#
x
c + ln x
x
y0
The inter
Math 33B: Differential Equations
Practice problems for final
December 2014
Instructor: aliki
This handout includes 10 problems to help you prepare for the final.
There are more Topic 1 problems as I thought Topics 2 & 3 are still fresh
in your mind. The
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Final Review
UCLA Math 33A Exam #1
Review and Problems
January 2015
1
Overview
Exam #1 will focus on material covered in lectures 1-7
You should be be able solve ODEs using the following techniques:
separation of variables
integrating factors
exact ODEs and exact
UCLA Math 33A Exam #2
Review
February 2015
Overview
Exam #2 will focus on material covered in lectures 8-15
You should review material on autonomous systems and stability from section 2.9 of your
textbook.
Homogeneous second order ODEs:
The second ord
NOTES ON THE MATRIX EXPONENTIAL.
MATT
Some notes on the matrix exponential, and what to do with it. I recommend doing exercises in
the text, and always trying to stop frequently to test your understanding. Not to repeat your high
school English teachers s
UCLA Math 33BiExam #27Winter 2015 1
1. (12 points) Consider the rst order ODE ,
<13x2>j_:$ (1)
(a) (6 points) Find all equilibrium solutions to (1), and for each solution determine Whether
it is stable or not.
Romulwx (0 as at GUIXMIHC) we slay-Mat
at H
NOTES FOR 2/10/15 SECTION 1C: I.E. WHAT YOU SHOULD DO WHEN
YOU ENCOUNTER A SECOND-ORDER LINEAR ODE
MATT
1. Second-Order Linear ODE
What should you do when you are confronted by an equation of the form:
y 00 + p(t)y 0 + q(t)y = f (t)?
(1)
1.1. If f (t) = 0
Repeated Eigenvalues
So far, what we have seen about first-order systems of two equations
parallels what we already knew about second-order single equations.
There is a characteristic polynomial, whose roots give exponential
functions that form the basi
NOTES ON SOME MIDTERM 2 TEST QUESTIONS.
MATT
Brief solutions to problems 1,3,4.
1. Problem 1
Problem. Consider the first order ODE
1
dx
)
= x.
2
1 x dt
a) Find all equilibrium solutions to (1). For each solution, determine whether it is stable or not.
(1)
NOTES FOR 2/3/15 SECTION 1C
MATT
These are notes from Section on Tuesday, 2/3. We do the formula for solving second-order linear
equations. We write down the definition of C . Finally, I got around to writing down the proof
of the Existence-Uniqueness The