Question

Find a particular solution satisfying the given condition `- cos((dy)/(dx)) = a, (a ∈ R), y` = 1 when `x` = 0

Options

• `sec x`

• `tan x  dx`

• `(cos  y - 2)/x`

• None of these

Answer 1

`(cos  y - 2)/x`

Explanation:

`cos  ((dy)/(dx)) = a` 

∴ `(dy)/(dx) = - cos^-1a`

or `dy = (cos a) dx`

Integrating, `int dy = (cos^-1 a) int  dx` or `y = (cos^-1 a)x + c`

We have `y` = 2, when `x` = 0 ⇒ 2 = `c`

∴ Solution is `y = x(cos^-1 a) + 2` or `cos^-1a = (y - 2)/x`

`a = cos  (y - 2)/x` is the required solution.