Which of these functions is homogeneous of degree 0?

\frac{\sin y}{x}

Correct answerYour answer

x + y^{2}

Correct answerYour answer

y e^{x}

Correct answerYour answer

\sin{\left(\frac{y}{x} \right)}

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer D

Correct answer: D

$F$ is homogeneous of degree $n$ when $F(\lambda x, \lambda y) = \lambda^{n} F(x, y)$ .
$\sin{\left(\frac{y}{x} \right)}$ passes, with degree 0; each of the others fails.

Worth noting

$\frac{\sin y}{x}$ is not homogeneous: $\sin(\lambda y)$ is not a power of $\lambda$ times $\sin y$ .

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

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

Explanation