Match List – I with List – II.

Choose the correct answer from the options given below:

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

The correct answer is Option (3) - A-IV, B-I, C-II, D-III

(A) $\frac{d y}{d x}=e^{x-y}+x^2 e^{-y}⇒\frac{d y}{d x}=\frac{e^x+x^2}{e^y}$

so $\int e^ydy=\int e^x+x^2dx$ (IV)

(B) $\frac{d y}{d x}-2 y=\cos 3 x$ (I)

(C) $x^2 \frac{d y}{d x}=x^2-2 y^2+x y⇒\frac{d y}{d x}=1-2(\frac{y}{x})^2+(\frac{y}{x})=f(\frac{y}{x})$ (II)

(D) $\left(x+2 y^3\right) \frac{d y}{d x}=y$

so $\frac{dx}{dy}-\frac{x}{y}=2y^2$ (III)