Question

The differential equation whose solution is $Ax^2 + By^2 = 1$ where $A$ and $B$ are arbitrary constants is of

• A. second order and second degree
• B. first order and second degree
• C. first order and first degree
• D. second order and first degree

Answer 1

The Correct Option is D

$Ax^{2} + By^{2} = 1 $ .........(1)
$ Ax +By \frac{dy}{dx} = 0 $ .........(2)
$ A + By \frac{d^{2}y}{dx^{2}} + B \left(\frac{dy}{dx}\right)^{2} = 0$ ....(3)
From (2) and (3)
$ x \left\{ - By \frac{d^{2}y}{dx^{2}} - B \left(\frac{dy}{dx}\right)^{2}\right\} + By \frac{dy}{dx} = 0 $
Dividing both sides by $-B$, we get
$xy \frac{d^{2}y}{dx^{2}} + x \left(\frac{dy}{dx}\right)^{2} -y \frac{dy}{dx} = 0 $
Which is differential equation of order $2$ and degree $1$