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

AP Calculus ABmediummcq1 pt

What is the particular solution of $\dfrac{dy}{dx} = 4x$ that satisfies $y(1) = 5$ ?

A.

y = 2x^2 + 3

B.

y = 2x^2 + 5

C.

y = 4x^2 + 1

D.

y = 2x^2 - 1

Explanation

Core Concept

Integrating gives $y = 2x^2 + C$ ; substituting $(1,5)$ gives $5 = 2 + C$ , so $C = 3$ .

Correct Answer

A $y = 2x^2 + 3$

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