The order and degree of the differential equation ${\left[1+{\left(\frac{dy}{dx}\right)}^2+\sin \left(\frac{dy}{dx}\right)\right]}^{3/4}=\frac{d^{2}y}{d{x}^2}$ are:

1. Order: The highest derivative present is $\frac{d^{2}y}{d{x}^2}$, so the order is 2.2. Degree: The degree is the power of the highest derivative when the equation is a polynomial in its derivatives. Raising both sides to the power of 4 removes the fractional power:
$${\left[1+{\left(\frac{dy}{dx}\right)}^2+\sin \left(\frac{dy}{dx}\right)\right]}^3={\left(\frac{d^{2}y}{d{x}^2}\right)}^4$$
However, because of the $\sin \left(\frac{dy}{dx}\right)$ term, the equation cannot be expressed as a polynomial in derivatives. Therefore, the degree is not defined.