Which of these functions is homogeneous of degree 1?

\frac{x^{2} + y^{2}}{x + y}

Correct answerYour answer

\frac{x^{2} + y}{x + 1}

Correct answerYour answer

x y + 1

Correct answerYour answer

x^{2} - y^{3}

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer A

Correct answer: A

$F$ is homogeneous of degree $n$ when $F(\lambda x, \lambda y) = \lambda^{n} F(x, y)$ .
$\frac{x^{2} + y^{2}}{x + y}$ passes, with degree 1; each of the others fails.

Worth noting

$xy + 1$ has a constant term of degree 0 beside $xy$ of degree 2.

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

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

Explanation