Question

The degree and order of the differential equation `[1 + (dy/dx)^3]^(7/3) = 7((d^2y)/(dx^2))` respectively are ______.

Options

• 3 and 7

• 3 and 2

• 7 and 3

• 2 and 3

Answer 1

The degree and order of the differential equation `[1 + (dy/dx)^3]^(7/3) = 7((d^2y)/(dx^2))` respectively are 3 and 2.

Explanation:

The given differential equation is

`[1 + (dy/dx)^3]^(7/3) = 7((d^2y)/(dx^2))`

After cubing on both sides, we get

`[1 + (dy/dx)^3]^7 = 7^3((d^2y)/(dx^2))^3`

As, highest order derivative is 2, and its degree is 3.

Hence, degree = 3 and order = 2