The differential equation of the family of straight lines whose slope is equal to y-intercept is

A. $\frac{d y}{d x}=\frac{x-y}{y-1}$
B. $\frac{d y}{d x}=\frac{x+1}{y+1}$
C. $(x+1) \frac{d y}{d x}-y=0$
D. $(x+1) \frac{d y}{d x}+y=0$
E. $\frac{d y}{d x}-\frac{x+1}{y+1}=0$

Choose the correct answer from the given below:

C only

The correct answer is Option (3) - C only