If x=sint and y=cos pt, then

Options

A. `(1 - x^(2))y_(2) + xy_(1) p^(2) y = 0 `
B. `(1 - x^(2)) y_(2) + xy_(1)- p^(2)y = 0 `
C. `(1+x^(2)) y_(2) + xy_(1) - p^(2) y = 0 `
D. `(1 -x^(2)) y_(2)- xy_(1) + p^(2) y= 0 `

Answer

D

Explanation

Given , ` x = sin t , y = cos pt `
`(dx)/(dt) = cot t, (dy)/(dt) = - p sin pt `
` therefore (dy)/(dx) = - (p sin pt)/(cos t )`
`rArr y_(1) = (-psqrt(1-y^(2)))/(sqrt(1 - x)^(2))`
`rArry_(1) sqrt(1 -x^(2)) = - p sqrt(1- y^(2))`
`rArr y_(1) (1 - x^(2))= p^(2) (1-y^(2))`
` rArr 2y_(1)y_(2) (1-x^(2)) - 2xy_(1)^(2) = - 2yy_(1)p^(2)" " ` [differentiating ]
`rArr (1 - x^(2)) y_(2) - xy_(1) + p^(2) y = 0 ` .