An engineer's notes contain the equation √[3]x + (dy/dx)² = d²y/dx²…

Step 1. Clear the root. Cubing both sides gives $x + \left(\dfrac{dy}{dx}\right)^2 = \left(\dfrac{d^2y}{dx^2}\right)^3$.

Step 2. The order. The highest derivative is $\dfrac{d^2y}{dx^2}$, so the order is $2$.

Step 3. The degree. That derivative has the power $3$, so the degree is $3$.