For the following equations, determine its order, degree (if exists) ddddx2d2ydx2+[1+(dydx)2]12 = 0

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