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 d²y = 4x et dt? х 3 1 et cos(2t) + sin(2t) + -cos(2t) – sin(2t) - 5 When x = cos(2t) + sin(2t) + Let, dx dt d²x dt? When y = -cos(2t) – sin(2t) – ÷e', dy dt d?y dt? Thus, in terms of t, d?x 4y - et – 4(-cos(2t) – sin(2t) – e) - et dt? and d?y 4x + et 4( cos(2t) + sin(2t) + + et dt? II
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 d²y = 4x et dt? х 3 1 et cos(2t) + sin(2t) + -cos(2t) – sin(2t) - 5 When x = cos(2t) + sin(2t) + Let, dx dt d²x dt? When y = -cos(2t) – sin(2t) – ÷e', dy dt d?y dt? Thus, in terms of t, d?x 4y - et – 4(-cos(2t) – sin(2t) – e) - et dt? and d?y 4x + et 4( cos(2t) + sin(2t) + + et dt? II
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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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
d²y
= 4x
et
dt?
х 3
1 et
cos(2t) + sin(2t) +
-cos(2t) – sin(2t) -
5
When x = cos(2t) + sin(2t) + Let,
dx
dt
d²x
dt?
When y = -cos(2t) – sin(2t) – ÷e',
dy
dt
d?y
dt?
Thus, in terms of t,
d?x
4y - et
– 4(-cos(2t) – sin(2t) – e)
- et
dt?
and
d?y
4x + et
4( cos(2t) + sin(2t) +
+ et
dt?
II
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