The differential equation whose solution is $A x^2+B y^2=1$ where A and B are arbitrary constant is of:

(A) first order and first degree
(B) second order and first degree
(C) second order and second degree
(D) second order

Choose the correct answer from the options given below:

(B) and (D) Only

The correct answer is Option (3) - (B) and (D) Only

order = no. of arbitrary constants

$Ax^2+By^2=1$ differentiating wrt x

$2Ax+2By\frac{dy}{dx}=0⇒-Ax=By\frac{dy}{dx}$

so $\frac{y}{x}\frac{dy}{dx}=-A$

again differentiating

$\frac{y}{x}\frac{d^2y}{dx^2}+\frac{x\frac{dy}{dx}y}{x^2}\frac{dy}{dx}=0$

order = 2, degree = 1