1. Answer the following questions. d (A) [50%] Consider the non-homogeneous DE p y = F(x) where dx p(r) = r²(r + 2)³ (r²+4) and F(x) = 9+3xe¯2x − 5 sin(2x) + 12 cos(5x) Write the solution of the corresponding homogeneous DE (i.e., y(x)), and (without trying to determine the coefficients) write the general form of the particular solution yp(x). (B) [50%] Find the solution of the IVP 2y"7y+3yte-3t, y(0) = 0, y'(0) = 1. Then, to 4 decimals compute y(3.027). Find the long-time behaviour of the solution.
1. Answer the following questions. d (A) [50%] Consider the non-homogeneous DE p y = F(x) where dx p(r) = r²(r + 2)³ (r²+4) and F(x) = 9+3xe¯2x − 5 sin(2x) + 12 cos(5x) Write the solution of the corresponding homogeneous DE (i.e., y(x)), and (without trying to determine the coefficients) write the general form of the particular solution yp(x). (B) [50%] Find the solution of the IVP 2y"7y+3yte-3t, y(0) = 0, y'(0) = 1. Then, to 4 decimals compute y(3.027). Find the long-time behaviour of the solution.
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![1. Answer the following questions.
d
(A) [50%] Consider the non-homogeneous DE p
y = F(x) where
dx
p(r) = r²(r + 2)³ (r²+4) and F(x) = 9+3xe¯2x − 5 sin(2x) + 12 cos(5x)
Write the solution of the corresponding homogeneous DE (i.e., y(x)), and (without trying
to determine the coefficients) write the general form of the particular solution yp(x).
(B) [50%] Find the solution of the IVP
2y"7y+3yte-3t,
y(0) = 0, y'(0) = 1.
Then, to 4 decimals compute y(3.027). Find the long-time behaviour of the solution.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F86794e1d-a025-469e-9776-3458200614a7%2F18d763be-b29a-4a84-90eb-5d60b3dbf225%2F4e5gr1m_processed.png&w=3840&q=75)
Transcribed Image Text:1. Answer the following questions.
d
(A) [50%] Consider the non-homogeneous DE p
y = F(x) where
dx
p(r) = r²(r + 2)³ (r²+4) and F(x) = 9+3xe¯2x − 5 sin(2x) + 12 cos(5x)
Write the solution of the corresponding homogeneous DE (i.e., y(x)), and (without trying
to determine the coefficients) write the general form of the particular solution yp(x).
(B) [50%] Find the solution of the IVP
2y"7y+3yte-3t,
y(0) = 0, y'(0) = 1.
Then, to 4 decimals compute y(3.027). Find the long-time behaviour of the solution.
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