Which of these functions is homogeneous?

x^{2} + y

Correct answerYour answer

x^{2} + x y

Correct answerYour answer

x^{3} + y^{2}

Correct answerYour answer

x + \sin y

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer B

Correct answer: B

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

Worth noting

$x^{2} + y$ mixes degrees 2 and 1; every term must have the same degree.

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

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

Explanation