Question

The differential equation for which y = acosx + bsinx is a solution, is ______.

Options

• `("d"^2y)/("d"x^2) + y` = 0

• `("d"^2y)/("d"x^2) - y` = 0

• `("d"^2y)/("d"x^2) + ("a" + "b")y` = 0

• `("d"^2y)/("d"x^2) + ("a" - "b")y` = 0

Answer 1

The differential equation for which y = acosx + bsinx is a solution, is `("d"^2y)/("d"x^2) - y` = 0.

Explanation:

The given equation is y = acosx + bsinx

`("d"y)/("d"x)` = – asinx + bcosx

`("d"^2y)/("d"x^2)` = – acosx – bsinx

⇒ `("d"^2y)/("d"x^2)` = – (acosx + bsinx)

⇒ `("d"^2y)/("d"x^2)` = –y

⇒ `("d"y)/("d"x) + y` = 0