Match the Integrating factor of the following Differential equations.

Choose the correct answer from the options given below:

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

The correct answer is Option (1) → A-IV, B-I, C-II, D-III

(A) $\frac{d y}{d x}-y=\cos x⇒I.F.=e^{-1dx}=e^{-x}$ (IV)

(B) $\frac{dy}{dx}+y=\cos x⇒I.F.=e^{1dx}=e^{x}$ (I)

(C) $\frac{dy}{dx}+\frac{2}{x}y=x⇒I.F.=e^{\frac{2}{x}dx}=e^{\log x^2}=x^2$ (II)

(D) $\frac{dy}{dx}-\frac{2}{x}y=x⇒I.F.=e^{-\frac{2}{x}dx}=e^{\log \frac{1}{x^2}}=\frac{1}{x^2}$ (III)