A function is proposed as a potential solution of the differential equation dy dx =3…

MATHEMATICS · Multi-part · AP · Calculus AB · Differential Equations · Differential Equations

Problem

A function

y = x e^{2x}

is proposed as a potential solution of the differential equation

\frac{dy}{dx}=3 x e^{2x}

on the interval

(-\infty,\infty)

. (a) Compute

\dfrac{dy}{dx}

explicitly in terms of

x

for the given

y

. (b) Decide whether

y=x e^{2x}

satisfies the differential equation for all real

x

. Provide a clear justification that references your expression from part (a).