Question

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

Answer 1

$$\begin{gathered} \frac{d^{2}y}{d{x}^2}={\left(\frac{dy}{dx}\right)}^{\frac{2}{3}} \\ \mathrm{Taking}\mathrm{cubes}\mathrm{of}\mathrm{both}\mathrm{sides},\mathrm{we}\mathrm{get} \\ \Rightarrow {\left(\frac{d^{2}y}{d{x}^2}\right)}^3={\left(\frac{dy}{dx}\right)}^2 \end{gathered}$$

In this differential equation, the order of the highest order derivative is 2 and its power is 3. So, it is a differential equation of order 2 and degree 3.

It is a non-linear differential equation, as it has degree 3, which is greater than 1.