Determine whether the function satisfies the differential equation .

MATHEMATICS · Single correct · CBSE · Mathematics · Differential Equations · Differential Equations

Problem

Determine whether the function

y(x)=x e^{x}

satisfies the differential equation

\dfrac{dy}{dx}=x e^{x}+e^{x}

. (a) No, because differentiating gives

(x+1)e^{x}

, which is different from

x e^{x}+e^{x}

. (b) Yes, because

\dfrac{dy}{dx}=x e^{x}+e^{x}

for all

x

. (c) No, because

\dfrac{dy}{dx}=x e^{x}

, which lacks the extra

e^{x}

term. (d) Yes, because

\dfrac{dy}{dx}=2x e^{x}

, which equals

x e^{x}+e^{x}