Question

The degree of the differential equation `1/2 ("d"^3"y")/"dx"^3 = {1 + (("d"^2"y")/"dx"^2)}^(5/3)` is ______.

Options

• 1

• 15

• 3

• 9

Answer 1

The degree of the differential equation `1/2 ("d"^3"y")/"dx"^3 = {1 + (("d"^2"y")/"dx"^2)}^(5/3)` is 3.

Explanation:

`1/2 ("d"^3"y")/"dx"^3 = {1 + (("d"^2"y")/"dx"^2)}^(5/3)`

`=> 1/8 (("d"^3"y")/"dx"^3)^3 = {1 + (("d"^2"y")/"dx"^2)^3}^5`

Here, the highest order derivative is `("d"^3"y")/"dx"^3` with power 3.

∴ degree = 3