The Gateway to Computer Science Excellence
First time here? Checkout the FAQ!
x
+6 votes
948 views
The function $f(x) =x \sin x$ satisfies the following equation: $$f''(x) + f(x) +t \cos x = 0$$. The value of $t$ is______.
asked in Calculus by Veteran (112k points)
retagged by | 948 views

4 Answers

+19 votes
Best answer
$f'(x) =x\cos(x) + \sin(x)$

$f''(x)=x(-\sin x) +\cos x +\cos x$
 

now $f''(x)+f(x)+t \cos x= 0$

$ \Rightarrow x(-\sin x)+\cos x+\cos x+x\sin x+t\cos x=0$

$\Rightarrow 2\cos x+t\cos x = 0$
$\Rightarrow \cos x(t+2)=0$
$\Rightarrow t+2=0, t=-2$
answered by Active (4.9k points)
edited by
+4 votes

Hence, t = -2

answered by Active (1.6k points)
+2 votes
t=-2
answered by (329 points)
0
how?
+1 vote
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
answered by Loyal (8.8k points)
Answer:

Related questions



Quick search syntax
tags tag:apple
author user:martin
title title:apple
content content:apple
exclude -tag:apple
force match +apple
views views:100
score score:10
answers answers:2
is accepted isaccepted:true
is closed isclosed:true

44,493 questions
49,944 answers
165,712 comments
65,911 users