Which substitution turns a homogeneous equation dy/dx = F(y/x) into one with separable variables?

y = vx, with dy/dx = v + xdv/dx

y = v + x, with dy/dx = dv/dx + 1

Question 3

EasyOriginal question

Which substitution turns a homogeneous equation $\frac{dy}{dx} = F\left(\frac{y}{x}\right)$ into one with separable variables?

y = vx

, with

\frac{dy}{dx} = v

Correct answerYour answer

y = v + x

, with

\frac{dy}{dx} = \frac{dv}{dx} + 1

Correct answerYour answer

y = vx

, with

\frac{dy}{dx} = v + x\frac{dv}{dx}

Correct answerYour answer

y = \frac{v}{x}

, with

\frac{dy}{dx} = \frac{dv}{dx}

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer C

Correct answer: C

Worth noting

$\frac{dy}{dx} = v$ treats $v$ as a constant; it varies with $x$ .

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