Mathematics

Problem

Consider the family

y = x^{2} + Cx + 1

, where

C

is an arbitrary constant. Which of the following first-order differential equations is satisfied by every member of this family? a)

x\,\dfrac{dy}{dx} + y = x^{2} - 1

\dfrac{dy}{dx} = 2x + y

x\,\dfrac{dy}{dx} - y = x^{2} - 1

x\,\dfrac{dy}{dx} - y = x^{2}