The provided differential equation is: \[\left[ 1 + \left( \frac{dy}{dx} \right)^2 \right]^5 = \frac{d^2y}{dx^2}\]
To determine the order and degree, we identify the highest order derivative and its power.
* The highest derivative is \( \frac{d^2y}{dx^2} \), the second derivative. Thus, the order is 2.
* The power of the highest derivative term \( \frac{d^2y}{dx^2} \) is 1. Therefore, the degree is 1.
The order is 2 and the degree is 1.