GATE | GATE-CS-2014-(Set-1) | Question 56
The function f(x) = x sinx satisfies the following equation f”(x) + f(x) + t cosx = 0. The value of t is
(A) -1
(B) -2
(C) 1
(D) 2
Answer: (B)
Explanation:
We have f(x) = x sin x
⇒ f'(x) = x cos x + sin x
⇒ f′′(x) = x (− sin x ) + cos x + cos x = (−x sin x ) + 2 cos x
Now, it is given that f(x) = x sin x satisfies the equation f′′(x) + f(x) + t cos x = 0
⇒ (−x sin x ) + 2 cos x + x sin x + t cos x = 0
⇒ 2 cos x + t cos x = 0
⇒ cos x ( t + 2 ) = 0
⇒ t + 2 = 0
⇒ t = −2
Thus, B is the correct option.
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Last Updated :
28 Jun, 2021
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