Question

y = ae^mx+ be^–mx satisfies which of the following differential equation?

Options

• `("d"y)/("d"x) + "m"y` = 0

• `("d"y)/("d"x) - "m"y` = 0

• `("d"^2y)/("d"x^2) - "m"^2y` = 0

• `("d"^2y)/("d"x^2) + "m"^2y` = 0

Answer 1

`("d"^2y)/("d"x^2) - "m"^2y` = 0

Explanation:

The given equation is y = `"ae"^("m"x) + "be"^(-"m"x)`

On differentiation, we get `("d"y)/("d"x) = "a" . "me"^("m"x) - "b" . "m"e^(-"m"x)`

Again differentiating w.r.t., we have

`("d"^2y)/("d"x^2) = "am"^2 "e"^("m"x) + "bm"^2 "e"^(-"m"x)`

⇒ `("d"^2y)/("d"x^2) = "m"^2 ("ae"^("m"x) + "be"^(-"m"x))`

⇒ `("d"^2y)/("d"x^2) = "m"^2y`

⇒ `("d"^2y)/("d"x^2) - "m"^2y` = 0