Read the two statements and choose the correct option. I. dy/dx + y/x = y^2 is a linear differential equation in y. II. dy/dx = y/x + 2 is both homogeneous and linear.

Question 81

MediumOriginal question

Read the two statements and choose the correct option.
I. $\frac{dy}{dx} + \frac{y}{x} = y^{2}$ is a linear differential equation in $y$ .
II. $\frac{dy}{dx} = \frac{y}{x} + 2$ is both homogeneous and linear.

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

Show the answer and explanation

CorrectNot quiteAnswer B

Correct answer: B

I: the $y^{2}$ on the right makes it non-linear in $y$ . False.
II: the right side is $v + 2$ , a function of $\frac{y}{x}$ , and $\frac{dy}{dx} - \frac{1}{x}y = 2$ is linear. True.

Worth noting

One equation can fit both methods: being homogeneous and being linear are separate tests.

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