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

AP Calculus ABeasymcq1 pt

Which of the following is a solution to the differential equation $\dfrac{dy}{dx} = 2xy$ ?

A.

y = 5e^{x^2}

B.

y = 5e^{2x}

C.

y = x^2 + 5

D.

y = \dfrac{5}{2}x^2

Explanation

Core Concept

Differentiating gives $y' = 5e^{x^2}\cdot 2x = 2x\cdot 5e^{x^2} = 2xy$ , which matches the differential equation.

Correct Answer

A $y = 5e^{x^2}$

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