Question

The integrating factor of the differential equation sin y `("dy"/"dx")` = cos y(1 - x cos y) is ______.

Options

• e^{sin y}

• e^-x

• `e^(-cos y)`

• e^-y

Answer 1

The integrating factor of the differential equation sin y `("dy"/"dx")` = cos y(1 - x cos y) is e^-x.

Explanation:

We have,

`sin y "dy"/"dx"` = cos y (1 - x cos y)

tan y `"dy"/"dx"` = 1 - x cos y

tan y `"dy"/"dx" - 1` = - x cos y

sec y tan y `"dy"/"dx"` - sec y = - x

Put, sec y = z

∴ sec y tan y `"dy"/"dx" = "dz"/"dx"`

∴ `"dz"/"dx"` - z = - x

∴ IF = `"e"^(int - "dx") = "e"^(- x)`