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

AP Calculus ABeasymcq1 pt

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

A.

y = e^x - 1

B.

y = e^x

C.

y = e^x + 1

D.

y = 1 - e^{-x}

Explanation

Core Concept

$y' = e^x$ , and $y + 1 = e^x$ , so the equation holds; also $y(0) = 1 - 1 = 0$ .

Correct Answer

A $y = e^x - 1$

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