Verify that the indicated pair of functions is a solution of the given syste d2x 4y + et dzy = 4x - et x = cos(2t) + sin(2t) + 5 1 t y = -cos(2t) - sin(2t) 5 – e When x = cos(2t) + sin(2t) + dx dt d?x = dt2 1 t When y = -cos(2t) – sin(2t) – e“, 5 dy dt dt2 Thus, in terms of t, d?x 4y - et 1 t (-cos(2t) – sin(2t) - e) - e dt2 5

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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Verify that the indicated pair of functions is a solution of the given system of differential equations on the interval (-, ∞).
d?x
= 4y + et
dt2
= 4x - e
dt2
x = cos(2t) + sin(2t) +
1
y = -cos(2t)
sin(2t) – e
-
When x = cos(2t) + sin(2t) +
dx
dt?
When y =
-cos(2t) – sin(2t) - e",
dy
dt
dzy
dt?
Thus, in terms of t,
d?x
- 4(-cos(2t) – sin(2t) -e)
4y -
dt2
and
-4(cos(2t) + sin(24) + 방) + e°
4x + e'
dt2
Transcribed Image Text:Verify that the indicated pair of functions is a solution of the given system of differential equations on the interval (-, ∞). d?x = 4y + et dt2 = 4x - e dt2 x = cos(2t) + sin(2t) + 1 y = -cos(2t) sin(2t) – e - When x = cos(2t) + sin(2t) + dx dt? When y = -cos(2t) – sin(2t) - e", dy dt dzy dt? Thus, in terms of t, d?x - 4(-cos(2t) – sin(2t) -e) 4y - dt2 and -4(cos(2t) + sin(24) + 방) + e° 4x + e' dt2
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