Question

The differential equation whose solution is y = Ae^x + Be^-x, is

विकल्प

• `("d"^2"y")/"dx"^2` + y = 0

• `("d"^2"y")/"dx"^2` - y = 0

• `"dy"/"dx"` + y = 0

• `"dy"/"dx"` - y = 0

Answer 1

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

Explanation:

y = Ae^x + Be^-x   ....(i)

`=> "dy"/"dx"` = Ae^x - Be^-x

`=> ("d"^2"y")/"dx"^2` = Ae^x + Be^-x 

= y   ...[from (i)]

∴ `("d"^2"y")/"dx"^2` - y = 0