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

AP Calculus ABeasymcq1 pt

Which of the following is the general solution of the differential equation $\dfrac{dy}{dx} = 3y$ ?

A.

y = Ce^{3x}

B.

y = Ce^{-3x}

C.

y = 3e^{x} + C

D.

y = e^{3x} + C

Explanation

Core Concept

Separating variables gives $\dfrac{dy}{y} = 3\,dx$ , and integrating yields $\ln|y| = 3x + C$ , so $y = Ce^{3x}$ .

Correct Answer

A $y = Ce^{3x}$

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