Consider the curve which is represented by the differential equation $\frac{dy}{dx}=1+x+y+ xy$. If it passes through the point (0, 0), then which of the following is/are true?

(A) it is a straight line.
(B) it is a parabola.
(C) it also passes through the point $(-1,\frac{1}{\sqrt{e}},-1)
(D) Its equation is $xy(x + 1)(y − \frac{1}{\sqrt{e}} + 1) = 0$

Choose the correct answer from the options given below:

(C) only

The correct answer is Option (4) → (C) only

(A) it is a straight line. (False)
(B) it is a parabola. (False)
(C) it also passes through the point $(-1,\frac{1}{\sqrt{e}},-1)$ (True)
(D) Its equation is $xy(x + 1)(y − \frac{1}{\sqrt{e}} + 1) = 0$ (False)