Show that the general solution of differential equation dy/dx + (y^2 + y +1)/(x^2 + x +1) = 0

Question

Show that the general solution of differential equation.

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

dy/dx + (y² + y +1)/(x² + x +1)

is given by (x + y + 1) = c(1 – x – y – 2xy).

Answer 1

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

Integrating both sides, we get

This is the general solution.