Question

For the following equations, determine its order, degree (if exists)

`x^2 ("d"^2y)/("d"x^2) + [1 + (("d"y)/("d"x))^2]^(1/2)` = 0

Answer 1

`x^2 ("d"^2y)/("d"x^2) - [1 + (("d"y)/("d"x))^2]^(1/2)` 

On squaring both sides, we get

`x^4(("d"^2y)/("d"x^2))^2 = [1 + (("d"y)/("d"x))^2]`

`x^4(("d"^2y)/("d"x^2))^2 = 1 + (("d"y)/("d"x))^2`

In this equation

The highest order derivative is `("d"^2y)/("d"x^2)` and its power is 2.

∴ Its order = 2 and degree = 2