This question was previously asked in

Airforce Group X 5 November 2020 Memory Based Paper

Option 4 : 2

__Concept:__

Order: The order of a differential equation is the order of the highest derivative appearing in it.

Degree: The degree of a differential equation is the power of the highest derivative occurring in it, after the Equation has been expressed in a form free from radicals as far as the derivatives are concerned.

__Calculation:__

Given:

\(\rm y = x \dfrac{dy}{dx}+\left(\dfrac{dy}{dx}\right)^{2} \)

For the given differential equation the highest order derivative is 1.

Now, the power of the highest order derivative is 2.

We know that, the degree of a differential equation is the power of the highest derivative

Hence, the degree of the differential equation is 2.