Which of these functions is homogeneous?

e^{x y}

Correct answerYour answer

x + e^{y}

Correct answerYour answer

x e^{\frac{y}{x}}

Correct answerYour answer

y + \log x

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer C

Correct answer: C

Replace $x, y$ by $\lambda x, \lambda y$ ; a homogeneous function gives back $\lambda^{n}$ times itself.
$x e^{\frac{y}{x}}$ gives $\lambda^{1}$ times itself; each of the others fails.

Worth noting

$e^{xy}$ becomes $e^{\lambda^{2}xy}$ , which is no power of $\lambda$ times $e^{xy}$ .

Ten questions from Homogeneous & Linear Differential Equations, at your own pace.

Ten questions from Homogeneous & Linear Differential Equations, at your own pace.

Explanation