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

AP Calculus ABmediummcq1 pt

Which of the following functions satisfies $\dfrac{dy}{dx} = \dfrac{x}{y}$ and $y(0) = 1$ ?

A.

y = \sqrt{x^2 + 1}

B.

y = \sqrt{x^2 - 1}

C.

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

D.

y = \sqrt{x^2 + 2}

Explanation

Core Concept

Differentiating gives $y' = \dfrac{x}{\sqrt{x^2+1}} = \dfrac{x}{y}$ , and $y(0) = \sqrt{1} = 1$ .

Correct Answer

A $y = \sqrt{x^2 + 1}$

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