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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