Question

The differential equation of the family of curves y = `"ae"^(2(x + "b"))` is ______.

Options

• `"dy"/"dx" - "y" = 0`

• `"dy"/"dx" + "y" = 0`

• `"dy"/"dx" + "2y" = 0`

• `"dy"/"dx" - "2y" = 0`

Answer 1

The differential equation of the family of curves y = `"ae"^(2(x + "b"))` is `underline("dy"/"dx" - "2y" = 0)`.

Explanation:

y = `"ae"^(2(x + "b"))`     ...(i)

`=> "dy"/"dx" = 2"ae"^(2(x + "b"))`

`=> "dy"/"dx" = "2y"`     ....[From(i)]

`=> "dy"/"dx" - 2"y"` = 0