Question

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

`y(("d"y)/("d"x)) = x/((("d"y)/("d"x)) + (("d"y)/("d"x))^3`

Answer 1

`y("d"y)/("d"x) = x/(("d"y)/("d"x) + (("d"y)/("d"x))^3`

`y ("d"y)/("d"x)[("d"y)/("d"x) + (("d"y)/("d"x))^3]` = x

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

In this equation

The highest order derivative is `("d"y)/("d"x)` and its power is 4.

∴ Its order = 1 and degree =