Answer 1

Since, 
The given differential equation is

`((d^4"y")/(d"x"^4))^2 =  [ "x" + ((d"y")/(d"x"))^2]^3`

`((d^4"y")/(d"x"^4))^2 = "x"^3 + ((d"y")/(d"x"))^6 + 3"x"^2 ((d"y")/(d"x"))^2 + 3"x" ((d"y")/(d"x"))^4` 

The highest order derivative in the differential equation is `(d^4"y")/(d"x"^4)` ⇒ Order of the given differential equation is 4.
The highest power raised to `(d^4"y")/(d"x"^4)` is 2⇒ Degree of the given differential equation is 2.