Match List I with List II

Choose the correct answer from the options given below :

A-IV, B-III, C-II, D-I

The correct answer is Option (2) → A-IV, B-III, C-II, D-I

(A) $3y^2\frac{dy}{dx}-3y^2-6xy\frac{dy}{dx}=3x^2+3x^2\frac{dy}{dx}+6xy$

$⇒\frac{dy}{dx}=\frac{(x+y)^2}{y^2-2xy-x^2}$

(B) $\frac{dy}{dx}=\frac{d(x^x)}{dx}=y(1+\log x)$

(C) $\frac{dy}{dx}=\frac{1-\log x}{x^2}⇒\frac{d^2y}{dx^2}=\frac{2\log x-3}{x^2}$

(D) $\frac{dy}{dx}=3x^2\log x+x^2=x(1+3x\log x)$