What are the order and degree, respectively of the differential equation ${\left(\frac{d^{2}y}{d{x}^2}\right)}^{5/6}={\left(\frac{dy}{dx}\right)}^{1/3}?$

Given differential equation is: 

   ${\left(\frac{d^{2}y}{d{x}^2}\right)}^{5/6}={\left(\frac{dy}{dx}\right)}^{1/3}$

Raising both the side to power of 6, to make it a polynomial of derivatives. 

  $$\begin{gathered} \Rightarrow {\left(\frac{d^{2}y}{d{x}^2}\right)}^5={\left(\frac{dy}{dx}\right)}^{6/3} \\ \Rightarrow {\left(\frac{{\mathrm{d}}^2\mathrm{y}}{{\mathrm{dx}}^2}\right)}^5={\left(\frac{\mathrm{dy}}{\mathrm{dx}}\right)}^2 \end{gathered}$$

Highest derivative has power of 5. So, the order and degree of given differential equation are 2 and 5 respectively.