What is the degree of the differential equation ${\left(\frac{d^{3}y}{d{x}^3}\right)}^{3/2}+{\left(\frac{d^{2}y}{d{x}^2}\right)}^2=0$?

The degree of a differential equation is the power of the highest order derivative when the equation is expressed as a polynomial in derivatives (i.e., powers must be positive integers).Given:
$${\left(\frac{d^{3}y}{d{x}^3}\right)}^{3/2}=-{\left(\frac{d^{2}y}{d{x}^2}\right)}^2$$
To remove the fractional power, square both sides:
$${\left[{\left(\frac{d^{3}y}{d{x}^3}\right)}^{3/2}\right]}^2={\left[-{\left(\frac{d^{2}y}{d{x}^2}\right)}^2\right]}^2$$
$${\left(\frac{d^{3}y}{d{x}^3}\right)}^3={\left(\frac{d^{2}y}{d{x}^2}\right)}^4$$
The highest order derivative is $\frac{d^{3}y}{d{x}^3}$. Its power is $3$.Therefore, the degree is $3$.