GATE 2014 CS (CS1) – Question 56
The function $f(x)=x\sin x$ satisfies $f^{\prime\prime}(x)+f(x)+t\cos x=0$. Find t.
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Correct answer: -2 to -2
Explanation
For f=xsinx, f′=sinx+xcosx and f″=2cosx−xsinx. Therefore f″+f=2cosx. The identity f″+f+tcosx=0 requires **t=−2** for all x, including points where cosx is nonzero.