Question

The solution of the differential equation `("d"y)/("d"x) + 2y tan x = 2x cos^2x` is ______.

पर्याय

• y sec²x = x² + c

• y sec x = c

• y cosec x² = c

• y sec x² = c

Answer 1

The solution of the differential equation `("d"y)/("d"x) + 2y tan x = 2x cos^2x` is y sec²x = x² + c.

Explanation:

 `("d"y)/("d"x) + 2y tan x = 2x cos^2x`

∴ I.F. = `"e"^(2int tanx  "d"x)`

= `"e"^(2log secx)`

= `sec^2x`

∴ Solution of the given equation is

`y* sec^2x = int 2x sec^2x* cos^2x  "d"x + "c"`

⇒ `y sec^2x = int 2x  "d"x + "c"`

⇒ y sec²x = x² + c