Question

Determine the order and degree of the following differential equation:

`(("d"^3"y")/"dx"^3)^2 = root(5)(1 + "dy"/"dx")`

Answer 1

The given D.E. is

`(("d"^3"y")/"dx"^3)^2 = root(5)(1 + "dy"/"dx")`

`(("d"^3"y")/"dx"^3)^(2xx5) = 1 + "dy"/"dx"`

`(("d"^3"y")/"dx"^3)^10 = 1 + "dy"/"dx"`

This D.E. has highest order derivative `("d"^3"y")/"dx"^3` with power 10.

∴ the given D.E. is of order 3 and degree 10.