The order and degree of the differential equation (d⁴y/dx⁴)² + (dy/dx)⁸ + 9y = log(x) is-

order 4, degree 2

The order of the differential equation is the order of the highest derivative involve in the differential equation so the order of the differential equation 

(d⁴y/dx⁴)² + (dy/dx)⁸ + 9y = log(x)  is 4.

The degree of the  differential equation is equal to the power of the highest derivative involve in the equation so the degree of the given differential equation (d⁴y/dx⁴)² + (dy/dx)⁸ + 9y = log(x)  is 2.