Let , where is a real constant. For which value of does satisfy the differential…

MATHEMATICS · Subjective · AP · Calculus AB · Differentiation: Composite, Implicit, and Inverse Functions · Differentiation: Composite, Implicit, and Inverse Functions

Problem

Let

y=(k x + 3)\, e^{x^{2}}

, where

k

is a real constant. For which value of

k

does

y

satisfy the differential equation

\dfrac{dy}{dx} = (6x^{2}+6x+3)\, e^{x^{2}}

? Provide the value of

k

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