Read the two statements and choose the correct option. I. If f and g are homogeneous of degrees 3 and 1, then f/g is homogeneous of degree 2. II. If f and g are homogeneous of degrees 2 and 1, then f + g is homogeneous of degree 3.

Question 19

MediumOriginal question

Read the two statements and choose the correct option.
I. If $f$ and $g$ are homogeneous of degrees 3 and 1, then $\frac{f}{g}$ is homogeneous of degree 2.
II. If $f$ and $g$ are homogeneous of degrees 2 and 1, then $f + g$ is homogeneous of degree 3.

Only ICorrect answerYour answerOnly IICorrect answerYour answerBoth I and IICorrect answerYour answerNeither I nor IICorrect answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer A

Correct answer: A

I: $\frac{\lambda^{3}f}{\lambda g} = \lambda^{2}\frac{f}{g}$ . True.
II: $x^{2} + x$ is such a sum, and $\lambda^{2}x^{2} + \lambda x$ is no power of $\lambda$ times it, so it is not homogeneous at all. False.

Worth noting

Degrees add for a product; a sum of terms of different degrees has no single degree.

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