Question

y = 3 cos 2x is a solution of the differential equation

Options

• `"dy"/"dx" + "6y" = 0`

• `"dy"/"dx" - "6y" = 0`

• `("d"^2"y")/"dx"^2 + 4"y" = 0`

• `("d"^2"y")/"dx"^2 - 4"y" = 0`

Answer 1

("d"^2"y")/"dx"^2 + 4"y" = 0`

Explanation:

y = 3 cos 2x     ...(i)

`=> "dy"/"dx"` = - 6 sin 2x

`=> ("d"^2"y")/"dx"^2` = - 12 cos 2x = - 4 × 3 cos 2x = - 4y    ....[from (i)]

`=> ("d"^2"y")/"dx"^2` + 4y = 0