Question

Solution of `sinx dy/dx + y cosx = 1` is ______ 

Options

• y + sec x tan x = c

• y sin x = x + c

• y tan x = sec x + c

• y sin x = sec x tan x + c

Answer 1

Solution of `sinx dy/dx + y cosx = 1` is y sin x = x + c.

Explanation:

 `sinx dy/dx + y cosx = 1`

⇒ `dy/dx + ycotx = cosecx`

∴ I.F. = `e^{intcotx dx} = e^{log sinx} = sinx`

∴ solution of the given equation is

`y sinx = int1 dx + c = x + c`