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If (dy)/(dx) + (4)/(cos^2 x) y = (1)/(co...

If (dy)/(dx) + (4)/(cos^2 x) y = (1)/(cos^2 x) , x in ((-pi)/(3) , pi/3) " and " y (pi/6) = 4/3 " then " y (- pi/6) ` equals ,

A

`1/4 + 13/12 e^(8/sqrt3)`

B

`1/4 + 13/12 e^(4/sqrt3)`

C

`4/3`

D

`(-4)/(3)`

Text Solution

Verified by Experts

The correct Answer is:
A
IF `= e^(int 4 sec^2 xdx) = e^(4 tan x)`
` y xx e^(4 tan x) = int sec^2 x e^(4 tan x) dx + c`
` y xx e^(4 tan x) = 1/4 e^(4 tan x + c)`
` y xx e^(+4//sqrt3) = 1/4 e^(+ 4 xx 1 // sqrt3) + c`
`4/3 xx e^(+4 // sqrt3) - 1/4 e^(+4 // sqrt3) = c`
` 13/12 xx e^(+4 // sqrt3) = c `
` y = 1/4 + (13/12 xx e^(+ 4 // sqrt3) )/(e^(-4// sqrt3) ) `
` y = 1/4 + 13/12 e^(8//sqrt3) `
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