The differential equation $y=xp+\sqrt{x^2p^3+4}$ where $p=\frac{dy}{dx} $ is :

(A) of order 1

(B) of degree 1

(C) of order 2

(D) of degree 3

Choose the correct answer from the options given below :

(A) and (D) Only

$y = xp + \sqrt{x^2p^3 + 4}, \quad p=\frac{dy}{dx}.$

$\text{Highest order derivative present is } \frac{dy}{dx}.$

$\text{Order} = 1.$

$y-xp=\sqrt{x^2p^3+4}.$

$(y-xp)^2 = x^2p^3+4.$

$\text{This is a polynomial in }p \text{ with highest power } p^3.$

$\text{Degree} = 3.$

$\text{Correct options: (A) order 1 and (D) degree 3.}$