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CGP EDU Academic Team
Published on: August 13, 2026
If y = e –x cos x and y n + k n y = 0 where y n = 
and k n , are constants ∀ n ∈ N.
Text Solution
Verified by ExpertsThe correct answer is:
CHECK THE SOLUTION.
(a, b)
y = e –x cos x
y 1 = – e –x cos x – e –x sin x = – 
e –x cos 
y 2 = + ( 
) 2 e –x cos 
y 3 = (– 
) 3 e –x cos 
y 4 = + ( 
) 4 e –x cos (x – π ) = – 4 e –x cos x
⇒ y 4 + 4y = 0 ⇒ k 4 = 4
Differentiating it again 4 times
y 8 + 4y 4 = 0 ⇒ y 8 – 16y = 0 ⇒ k 8 = – 16
y 12 + 4y 8 = 0 ⇒ y 12 + 64y = 0 ⇒ k 12 = 64
Similarly k 16 = – 256
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