Which of the following functions satisfies the differential equation for all real numbers

MATHEMATICS · Single correct · AP · Calculus AB · Differential Equations · Differential Equations

Problem

Which of the following functions

y=y(x)

satisfies the differential equation

\dfrac{dy}{dx}=2x\,y

for all real numbers

x

? (Here

C

denotes a non-zero constant.) (a)

y=Ce^{2x}

(b)

y=Ce^{-x^{2}}

(c)

y=Ce^{x^{2}}

(d)

y=Ce^{x^{2}/2}