Consider the nonhomogeneous equation: y" + by' + y = g(æ) %3D 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? (d) Explain why you will never need more than three guesses.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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5.
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?
(d) Explain why you will never need more than three guesses.
Transcribed Image Text:5. 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? (d) Explain why you will never need more than three guesses.
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