Question

\[\left( \frac{dy}{dx} \right)^2 + \frac{1}{dy/dx} = 2\]

Answer 1

\[\left( \frac{dy}{dx} \right)^2 + \frac{1}{\left( \frac{dy}{dx} \right)} = 2\]

\[\Rightarrow \frac{\left( \frac{dy}{dx} \right)^3 + 1}{\left( \frac{dy}{dx} \right)} = 2\]

\[\Rightarrow \left( \frac{dy}{dx} \right)^3 - 2\frac{dy}{dx} + 1 = 0\]
In this equation, the order of the highest order derivative is 1 and its highest power is 3. So, it is a differential equation of order 1 and degree 3.

It is a non-linear differential equation because the differential coefficient \[\frac{dy}{dx}\]  has exponent 3, which is greater than 1.