Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy)
4th Edition
ISBN: 9780133178579
Author: Ross L. Finney
Publisher: PEARSON
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Question
Chapter 10.3, Problem 35E
(a)
To determine
Whether it is possible to find a formula for the function y that does not involve any integrals.
(a)
Expert Solution
Answer to Problem 35E
No, we cannot to find a formula for the function y that does not involve any integrals.
Explanation of Solution
Given information:
And
When
Since
Thus,
The differential equation cannot be solved for the formula of y.
However,
Only way to solve the differential equation is to write the series representation of
Then
Eliminate the constant term with the initial condition.
Therefore,
It is not possible to find a formula for the function y that does not involve any integrals.
(b)
To determine
Whether it is possible to represent y by a power series.
(b)
Expert Solution
Answer to Problem 35E
Yes, we can represent y with a power series.
Explanation of Solution
Given information:
And
When
We have
Integrate:
But
On putting
Therefore,
y can be represented by power series.
(c)
To determine
Values of x for the power series actually equal the function y.
(c)
Expert Solution
Answer to Problem 35E
Power series equals y for only
Explanation of Solution
Given information:
And
When
For some finite value of n,
The power series equals y when the error term is zero.
That occurs only for
According to the given initial condition,
For which
Therefore,
Power series equals y for only
Chapter 10 Solutions
Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy)
Ch. 10.1 - Prob. 1QRCh. 10.1 - Prob. 2QRCh. 10.1 - Prob. 3QRCh. 10.1 - Prob. 4QRCh. 10.1 - Prob. 5QRCh. 10.1 - Prob. 6QRCh. 10.1 - Prob. 7QRCh. 10.1 - Prob. 8QRCh. 10.1 - Prob. 9QRCh. 10.1 - Prob. 10QR
Ch. 10.1 - Prob. 1ECh. 10.1 - Prob. 2ECh. 10.1 - Prob. 3ECh. 10.1 - Prob. 4ECh. 10.1 - Prob. 5ECh. 10.1 - Prob. 6ECh. 10.1 - Prob. 7ECh. 10.1 - Prob. 8ECh. 10.1 - Prob. 9ECh. 10.1 - Prob. 10ECh. 10.1 - Prob. 11ECh. 10.1 - Prob. 12ECh. 10.1 - Prob. 13ECh. 10.1 - Prob. 14ECh. 10.1 - Prob. 15ECh. 10.1 - Prob. 16ECh. 10.1 - Prob. 17ECh. 10.1 - Prob. 18ECh. 10.1 - Prob. 19ECh. 10.1 - Prob. 20ECh. 10.1 - Prob. 21ECh. 10.1 - Prob. 22ECh. 10.1 - Prob. 23ECh. 10.1 - Prob. 24ECh. 10.1 - Prob. 25ECh. 10.1 - Prob. 26ECh. 10.1 - Prob. 27ECh. 10.1 - Prob. 28ECh. 10.1 - Prob. 29ECh. 10.1 - Prob. 30ECh. 10.1 - Prob. 31ECh. 10.1 - Prob. 32ECh. 10.1 - Prob. 33ECh. 10.1 - Prob. 34ECh. 10.1 - Prob. 35ECh. 10.1 - Prob. 36ECh. 10.1 - Prob. 37ECh. 10.1 - Prob. 38ECh. 10.1 - Prob. 39ECh. 10.1 - Prob. 40ECh. 10.1 - Prob. 41ECh. 10.1 - Prob. 42ECh. 10.1 - Prob. 43ECh. 10.1 - Prob. 44ECh. 10.1 - Prob. 45ECh. 10.1 - Prob. 46ECh. 10.1 - Prob. 47ECh. 10.1 - Prob. 48ECh. 10.1 - Prob. 49ECh. 10.1 - Prob. 50ECh. 10.1 - Prob. 51ECh. 10.1 - Prob. 52ECh. 10.1 - Prob. 53ECh. 10.1 - Prob. 54ECh. 10.1 - Prob. 55ECh. 10.1 - Prob. 56ECh. 10.1 - Prob. 57ECh. 10.1 - Prob. 58ECh. 10.1 - Prob. 59ECh. 10.1 - Prob. 60ECh. 10.1 - Prob. 61ECh. 10.1 - Prob. 62ECh. 10.1 - Prob. 63ECh. 10.1 - Prob. 64ECh. 10.1 - Prob. 65ECh. 10.1 - Prob. 66ECh. 10.1 - Prob. 67ECh. 10.1 - Prob. 68ECh. 10.1 - Prob. 69ECh. 10.1 - Prob. 70ECh. 10.1 - Prob. 71ECh. 10.1 - Prob. 72ECh. 10.1 - Prob. 73ECh. 10.1 - Prob. 74ECh. 10.1 - Prob. 75ECh. 10.1 - Prob. 76ECh. 10.2 - Prob. 1QRCh. 10.2 - Prob. 2QRCh. 10.2 - Prob. 3QRCh. 10.2 - Prob. 4QRCh. 10.2 - Prob. 5QRCh. 10.2 - Prob. 6QRCh. 10.2 - Prob. 7QRCh. 10.2 - Prob. 8QRCh. 10.2 - Prob. 9QRCh. 10.2 - Prob. 10QRCh. 10.2 - Prob. 1ECh. 10.2 - Prob. 2ECh. 10.2 - Prob. 3ECh. 10.2 - Prob. 4ECh. 10.2 - Prob. 5ECh. 10.2 - Prob. 6ECh. 10.2 - Prob. 7ECh. 10.2 - Prob. 8ECh. 10.2 - Prob. 9ECh. 10.2 - Prob. 10ECh. 10.2 - Prob. 11ECh. 10.2 - Prob. 12ECh. 10.2 - Prob. 13ECh. 10.2 - Prob. 14ECh. 10.2 - Prob. 15ECh. 10.2 - 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