In the context of differential equation

Match List I with List II

Choose the correct answer from the options given below:

A - III, B - IV, C - I, D - II

A. $\frac{d y}{d x}=\frac{1+y^2}{1+x^2}$

$\Rightarrow \frac{1}{1+y^2} d y=\frac{1}{1+x^2} d x$

⇒  III variable separable

B. $x^2 \frac{d y}{d x} =x^2-2 y^2+x y$

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

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

⇒  IV. Homogenous

C. sin x + y = cos (x + y)

⇒  I. Not a differential equation

D. $(x+y) \frac{d y}{d x}=1$

⇒  II. Linear first order