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

The order is the highest derivative present. Here, the highest derivative is $\frac{d^{2}y}{d{x}^2}$, so Order = 2.To find the degree, we must express the equation in a form free from radicals for the derivatives.Given: $x{\left(\frac{d^{2}y}{d{x}^2}\right)}^{2/3}=y^2{\left(\frac{dy}{dx}\right)}^{3/2}$ Raise both sides to the power of 6 (LCM of 3 and 2):
$${\left[x{\left(\frac{d^{2}y}{d{x}^2}\right)}^{2/3}\right]}^6={\left[y^2{\left(\frac{dy}{dx}\right)}^{3/2}\right]}^6$$
$$x^6{\left(\frac{d^{2}y}{d{x}^2}\right)}^4=y^{12}{\left(\frac{dy}{dx}\right)}^9$$
The power of the highest order derivative is 4.Thus, Order = 2 and Degree = 4.