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

AP Calculus ABhardmcq1 pt

What is the particular solution of $\dfrac{dy}{dx} = \dfrac{2x}{y}$ that satisfies $y(0) = 2$ ?

A.

y = \sqrt{2x^2 + 4}

B.

y = \sqrt{2x^2 + 2}

C.

y = 2x^2 + 2

D.

y = \sqrt{x^2 + 4}

Explanation

Core Concept

Separating gives $\dfrac{y^2}{2} = x^2 + C$ , so $y^2 = 2x^2 + 2C$ ; the condition $y(0)=2$ gives $2C = 4$ .

Correct Answer

A $y = \sqrt{2x^2 + 4}$

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