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Step 1: Identify the order of the differential equation.
The order of a differential equation is the highest order derivative present in the equation. In the given equation, $\frac{d^{2}y}{dx^{2}}$ is the highest order derivative, which is of order 2.
Step 2: Identify the degree of the differential equation.
The degree of a differential equation is the power of the highest order derivative, provided the equation is a polynomial equation in derivatives. However, in the given equation, $\frac{d^{2}y}{dx^{2}}$ is inside the $\sin$ function, which means the equation is not a polynomial equation in derivatives. Therefore, the degree is not defined.
Step 3: Determine the product of the order and degree.
Since the degree is not defined, the product of the order and degree is also not defined.
Correct Answer: not defined