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If y = 3 cos (log x) + 4 sin (log x), s...

If `y = 3 cos (log x) + 4 sin (log x)`, show that `x^2y_2+xy_1+y=0`

A

y

B

`=- xy`

C

-y

D

y

Text Solution

Verified by Experts

The correct Answer is:
C
Given , ` y = 3 cos (log x ) + 4 sin (log x) ` …(i)
On differentiating both sides w.r.t.x, we get
`(dy)/(dx) = y_(1) = - 3 sin (log x)(1)/(x) + 4 (log x) = (1)/(x)`
Again , differentiating both sides w.r.t.x, we get
` xy_(2) + y_(1) * 1 = - 3 cos (log x ) (1)/(x) - 4 sin (log x) (1)/(x)`
On multiplying throughout by x , we get
` x^(2) y_(2) + xy_(1) = - [ 3 cos (log x) + 4 sin (log x)]` [ from Eq. (i)]
`rArr x^(2) y_(2) + xy_(1) = - y`
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