Question

The order and degree of the differential equation `sqrt((dy)/(dx)) - 4 (dy)/(dx) - 7x = 0` are respectively ______.

Options

• `1 and 1/2`

• 2 and 1

• −1 and 1

• 1 and 2

Answer 1

The order and degree of the differential equation `sqrt((dy)/(dx)) - 4 (dy)/(dx) - 7x = 0` are respectively 1 and 2.

Explanation:

Given the difference equation is,

`sqrt((dy)/(dx)) - 4 (dy)/(dx) - 7 x = 0`

`sqrt((dy)/(dx)) = 4 (dy)/(dx) + 7x`

Squaring on both sides, we get

`(dy)/(dx) = 16((dy)/(dx))^2 + 49 x^2 + 56 x (dy)/(dx)`

Order = 1 and degree = 2