Apentix/AP Calculus AB/Unit 7: Differential Equations/Question

AP Calculus ABmediummcq1 pt

Which of the following is a solution to the differential equation $\dfrac{dy}{dx} = xy^2$ ?

A.

y = \dfrac{2}{1-x^2}

B.

y = 2e^{x}

C.

y = \dfrac{2}{x}

D.

y = 2x^2

Explanation

Core Concept

Using the chain rule, $y' = 2(1-x^2)^{-2}\cdot 2x = \dfrac{4x}{(1-x^2)^2}$ , and $xy^2 = \dfrac{4x}{(1-x^2)^2}$ , so the equation holds.

Correct Answer

A $y = \dfrac{2}{1-x^2}$

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