For which value of a is dy/dx = (2x + ay + a - 3)/(x + y) a homogeneous differential equation?

Homogeneous & Linear Differential Equations · Question 18 of 120

Question 18

MediumOriginal question

For which value of $a$ is $\frac{dy}{dx} = \frac{2x + ay + a - 3}{x + y}$ a homogeneous differential equation?

-3

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0

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2

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3

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CorrectNot quiteAnswer D

Correct answer: D

The bottom has degree 1, so every term on top must have degree 1: no constant term may remain.
The constant is $a - 3$ , so $a = 3$ , giving $\frac{2x + 3y}{x + y}$ of degree 0.

Worth noting

$a = 0$ removes the $ay$ term but leaves the constant $-3$ , of degree 0.

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

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