Question

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

Answer 1

\[\frac{d^2 y}{d x^2} = \left( \frac{dy}{dx} \right)^\frac{2}{3} \]
Taking cubes of both sides, we get
\[ \Rightarrow \left( \frac{d^2 y}{d x^2} \right)^3 = \left( \frac{dy}{dx} \right)^2\]
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.