Correct Answer - Option 1 : 2

__Concept:__

Degree of Differential Equation:

- The degree of the differential equation is represented by the power of the highest order derivative in the given differential equation.
- The differential equation must be a polynomial equation in derivatives for the degree to be defined.

**Calculation:**

\(\rm { {1 + {{\left( {\frac{{dy}}{{dx}}} \right)}^2}} } = {(\frac{{{d^2}y}}{{d{x^2}}})^2}\)

Here, the exponent of the highest order derivative is 2 (i.e. Second-order) and the given differential equation is a polynomial equation in derivatives.

Hence, the degree of this equation is 2.