Final answer:
The degree of the given differential equation is 2, since the highest derivative present is squared.
Step-by-step explanation:
The degree of the differential equation (d⁴ y/d x⁴)² + 3(d y/d x)³ - 3 x y = x² is determined by looking at the highest power of the highest derivative in the equation. In this case, the highest derivative is the fourth derivative of y with respect to x, and it is squared. Hence, the degree of this differential equation is 2, because (d⁴ y/d x⁴)² is raised to the second power.