Question

Find a particular solution, satisfying the condition `(dy)/(dx) = y tan x ; y = 1` when `x = 0`

Options

• `y = sec x`

• `y = tan x`

• `y = "cosec"  x `

• `y = cot x`

Answer 1

`y = sec x`

Explanation:

`(dy)/(dx) = y tan x` or `(dy)/(dx) = tan x dx`

Integrating we get,

`int (dy)/(dx) = int tan x dx`

`log y = - log cos x + log c`

or `log y + log cos x = log c`

or `log y cos x = c`

Putting `y = 1, x = 0` ⇒ `c = 1`

∴ `y cos x` = 1

or `y = sec x` is the solution.