August 31
section covered in text
1.2. Solutions and Initial Value Problems
objective
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to be able to determine whether given functions are
solutions to differential equations
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to be able to determine whether given functions are
solutions to initial value problems
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to be able to determine whether Theorem 1 implies
a given initial value problem has a unique solution
key ideas and/or vocabulary
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nth order differential equation :=
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explicit solution (defined on some interval)
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implicit solution
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Implicit Function Theorem
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initial value problem
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Theorem 1: existence and uniqueness of a solution
(first order, initial value)
solved problems-using key ideas
testing whether a function is an explicit
solution to a differential equation, #5,7
determining if a function is an implicit
solution to a differential equation, #2,9,13
one parameter family
of solutions, #17
finding solutions of the form f(x)
= emx, #20
using Theorem 1
to determine if there is a unique solution, #24,25
some problems have no solutions, #19
initial value problem with more than one solution,
#29
announcements
Homework: #1,8,12,15,16,21,26 (due
9/9 )
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QUESTION OF THE DAY
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Use the technique of partial fractions to evaluate  . |
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SOLUTION
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SOLUTION. Rewrite
the rational fraction as a sum of rational fractions.
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