1. (10 pts) Consider the dierential equation ty 3y = t5 t2 .
(a) (2 pts) For what points (t0 , y0 ) does the Existence and Uniqueness
Theorem guarantee that there exists one and only one solution to
this dierential equation satisfying the intial condition
33B-3 Practice Final Exam
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December 2, 2015
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This is a 3-hour closed-book exam. The textbook, lecture notes, and all personal scratch papers ar
PRACTICE MIDTERM 1
MATT
Problem 1
Find the value of a for which the ODE
x2 y + 3x2 + axy = 0
is exact, and then nd the general solution, using this value of a.
Problem 2
Given the initial value problem,
dx x
+ = 2, x(1) = 0
dt
t
Use an integrating factor
33B-3 Practice Midterm 1
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October 18, 2015
Instructions
This is a 50-minute closed-book exam. The textbook, lecture notes, and all personal scratch papers
33B-3 Practice Midterm 1
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I read, understood, and will follow the instructions given below.
Signature:
October 13, 2015
Instructions
This is a 50-minute closed-book exam. The textbook, lecture notes, and all personal scratch papers
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33B-3 Practice Midterm 2 Solution
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Signature:
November 17, 2015
Instructions
This is a 50-minute closed-book exam. The textbook, lecture notes, and all personal scrat