Question

The solution of `dy/dx + y cotx = cosecx` is ______ 

Options

• y sec³x = sec²x + c 

• y sec²x = x + c 

• y sinx = x + c

• y sin²x = x + c

Answer 1

The solution of `dy/dx + y cotx = cosecx` is y sinx = x + c

Explanation:

`dy/dx + ycotx = cosecx`

Here, P = cot x and Q = cosec x

∴ I.F. = `e^{intcotx dx}`

= `e^{log(sinx)} = sinx`

∴ solution of the given equation is

y (sin x) = `intsin x cosec  x  dx + c`

⇒ y sin x = `int 1  dx + c`

⇒ y sin x = x + c