Question

The order and degree of the differential equation `("d"^2y)/("d"x^2) = {y + (("d"^3y)/("d"x^3))^3}^(1/5)` are respectively ______.

Options

• 5 and 2

• 3 and 3

• 1 and 5

• 2 and 5

Answer 1

The order and degree of the differential equation `("d"^2y)/("d"x^2) = {y + (("d"^3y)/("d"x^3))^3}^(1/5)` are respectively 3 and 3.

Explanation:

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

⇒ `(("d"^2y)/("d"x^2)) = {[y + (("d"^3y)/("d"x^3))^3]^(1/5)}^3`

⇒ `(("d"^2y)/("d"x^2))^5 = y + (("d"^3y)/("d"x^3))^3`

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

∴ order = 3 and degree = 3