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 :
Answer & explanation
Correct answer: option 2
$y = xp + \sqrt{x^2p^3 + 4}, \quad p=\frac{dy}{dx}.$
$\text{Highest order derivative present is } \frac{dy}{dx}.$
$\text{Order} = 1.$
$y-xp=\sqrt{x^2p^3+4}.$
$(y-xp)^2 = x^2p^3+4.$
$\text{This is a polynomial in }p \text{ with highest power } p^3.$
$\text{Degree} = 3.$
$\text{Correct options: (A) order 1 and (D) degree 3.}$