Question

If m and n are respectively the order and degree of the differential equation `d/dx (dy/dx)^3 = 0` then the value of (m – n) is ______.

Options

• 0

• 1

• 2

• 3

Answer 1

If m and n are respectively the order and degree of the differential equation `d/dx (dy/dx)^3 = 0` then the value of (m – n) is 1.

Explanation:

Given: `d/dx (dy/dx)^3 = 0`

Differentiating `(dy/dx)^3` with respect to x, we get

`d/dx (dy/dx)^3 = 3 (dy/dx)^2 * (d^2y)/dx^2`

Order (m) = Highest derivative present is `(d^2y)/dx^2`.

m = 2

Degree (n) = Power of the highest derivative `(d^2y)/dx^2` is 1.

n = 1

m − n

= 2 − 1

= 1