The family of curves represented by `(dy)/(dx)=(x^(2)+x+1)/(y^(2)+y+1)` and the family represented by `(dy)/(dx)+(y^(2)+y+1)/(x^(2)+x+1)=0`

Options

A. Touch each other
B. Are orthogonal
C. Are one and the same
D. None of these

Explanation

To solve the given problem, we need to analyze the two differential equations provided:

1. \(\frac{dy}{dx} = \frac{x^2 + x + 1}{y^2 + y + 1}\)
2. \(\frac{dy}{dx} + \frac{y^2 + y + 1}{x^2 + x + 1} = 0\)

### Step 1: Rewrite the second differential equation

From the second differential equation, we can isolate \(\frac{dy}{dx}\):

\[ \frac{dy}{dx} = -\frac{y^2 + y + 1}{x^2 + x + 1} \]