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