17. Consider the nonhomogeneous equation: y" + by' + y = g(x) where b is a real constant. The following questions refer to your guess for yp using the method of undetermined coefficients. Do not solve for the coefficients. (a) If g(x) = 3x – 1, what is the first guess for y,? (b) Identify the value of b if g(x) = 7 sin x and you need your second guess for yp. What is that guess? (c) Identify the value of b if g(x) = 18e" and you need your third guess for Yp. What is that guess?
17. Consider the nonhomogeneous equation: y" + by' + y = g(x) where b is a real constant. The following questions refer to your guess for yp using the method of undetermined coefficients. Do not solve for the coefficients. (a) If g(x) = 3x – 1, what is the first guess for y,? (b) Identify the value of b if g(x) = 7 sin x and you need your second guess for yp. What is that guess? (c) Identify the value of b if g(x) = 18e" and you need your third guess for Yp. What is that guess?
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
Solve 17 a,b,c and d. Please solve all sub-question.
Transcribed Image Text:17. Consider the nonhomogeneous equation:
y" + by' + y = g(x)
where b is a real constant. The following questions refer to your guess for yp using the method of
undetermined coefficients. Do not solve for the coefficients.
(a) If g(x) = 3x – 1, what is the first guess for y,?
Yp?
(b) Identify the value of b if g(x) = 7 sin x and
you
need
your second guess
for
Yp.
What is that guess?
(c) Identify the value of b if g(x) = 18e* and
you need
your third guess
for
Yp.
What is that guess?
(d) Explain why you will never need more than three guesses.
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