Question

General solution of `("d"y)/("d"x) + ytanx = secx` is ______.

Options

• y secx = tanx + c

• y tanx = secx + c

• tanx = y tanx + c

• x secx = tany + c

Answer 1

General solution of `("d"y)/("d"x) + ytanx = secx` is y secx = tanx + c.

Explanation:

The given differential equation is `("d"y)/("d"x) + y tan x = secx`

Since, it is a linear differential equation

∴ P = tan x and Q = sec x

Integrating factor I.F. = `"e"^(int Pdx)`

= `"e"^(int tanx  "d"x)`

= `"e"^(log secx)`

= sec x

∴ Solution is `y xx "I"."F". = int "Q" xx "I"."F". "d"x + "c"`

⇒ `y xx secx = int secx * secx  "d"x + "c"`

⇒ `y sec x = int sec^2x  "d"x + "c"`

⇒ y secx = tanx + c