Consider the family

MATHEMATICS · Single correct · AP · Calculus AB · Differential Equations · Differential Equations

Problem

Consider the family y=x2+Cx+1y = x^{2} + Cx + 1, where CC is an arbitrary constant. Which of the following first-order differential equations is satisfied by every member of this family? (a) x dydx+y=x2−1x\,\dfrac{dy}{dx} + y = x^{2} - 1 (b) dydx=2x+y\dfrac{dy}{dx} = 2x + y (c) x dydx−y=x2−1x\,\dfrac{dy}{dx} - y = x^{2} - 1 (d) x dydx−y=x2x\,\dfrac{dy}{dx} - y = x^{2}

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