The particular solution of the differential equation `cos ((dy)/(dx)) = a, (a in R)` , satisfying the condition , y = 2 when x =0 is

Options

A. ` cos((y+2)/x)=a`
B. ` cos ((x+2)/y)=a`
C. ` cos((y-2)/x)=a`
D. `cos((x-2)/y)=a`

Answer

d

Explanation

Given , `cos ((dy)/(dx)) = a rArr (dy)/(dx) = cos^(-1)a`
On seperating the variables , we get `dy=(cos^(-1)a)dx`
On integrating both sides , we get `int dy = cos^(-1) a int dx`
` rArr y = cos^(-1) a (x) +C`
On putting y = 2 and x = 0 , we get , ` 2 = cos^(-1) (a) xx 0 +C`
` rArr C=2`
On substituting C = 2 in Eq. (i) ,we get
` y = x cos^(-1) a+2 rArr (y-2)/x = cos^(-1) a rArr cos ((y-2)/x) = a`