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

AP Calculus ABmediummcq1 pt

What is the particular solution of $\dfrac{dy}{dx} = 2xy$ that satisfies $y(0) = 3$ ?

A.

y = 3e^{x^2}

B.

y = 3e^{2x}

C.

y = e^{x^2} + 3

D.

y = 3x^2 + 3

Explanation

Core Concept

Separating gives $\ln|y| = x^2 + C$ , so $y = Ce^{x^2}$ ; the condition $y(0)=3$ forces $C = 3$ .

Correct Answer

A $y = 3e^{x^2}$

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