For the following equations, determine its order, degree (if exists) dddd(d2ydx2)3=1+(dydx)

Question

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

$(("d"^2y)/("d"x^2))^3 = sqrt(1 + (("d"y)/("d"x)))$

Answer 1

$(("d"^2y)/("d"x^2))^3 = sqrt(1 + (("d"y)/("d"x)))$

On squaring both sides, we get

$(("d"^2y)/("d"x^2))^(3 xx 2) = 1 + (("d"y)/("d"x))$

$(("d"^2y)/("d"x^2))^6 = 1 + ("d"y)/("d"x)$

In this equation

The highest order derivative is $("d"^2y)/("d"x^2)$ and its power is 6.

Its order = 2 and degree = 6