Match List - I with List - II.

LIST I Differential equation	LIST II Integrating Factor (I.F)
A. \(\frac{d y}{d x}-\frac{y}{x}=2 x\)	I. \(x^2-1\)
B. \(\frac{d y}{d x}+\left(\frac{2 x}{x^2-1}\right) y=\frac{2}{\left(x^2-1\right)^2}\)	II. \(\sqrt{1-x^2}\)
C. \(\frac{d y}{d x}-\left(\frac{x}{1-x^2}\right) y=\frac{1}{1-x^2}\)	III. \(\frac{1}{x}\)
D. \(\frac{d y}{d x}+\frac{2 x y}{1+x^2}=\frac{\cot x}{1+x^2}\)	IV. \(1+x^2\)

Choose the correct answer from the options given below:

1. A (A)-(III), (B)-(I), (C)-(IV), (D)-(II)
2. B (A)-(III), (B)-(IV), (C)-(I), (D)-(II)
3. C (A)-(III), (B)-(II), (C)-(I), (D)-(IV)
4. D (A)-(III), (B)-(I), (C)-(II), (D)-(IV)