Written as dy/dx = F, what is F in terms of v…

Written as dy/dx = F, what is F in terms of v = y/x?

Question 31

EasyOriginal question

Consider the differential equation $x^{2}\frac{dy}{dx} = x^{2} + xy + y^{2}$ , and put $y = vx$ .

Written as $\frac{dy}{dx} = F$ , what is $F$ in terms of $v = \frac{y}{x}$ ?

v + v^{2}

Correct answerYour answer

1 + v^{2}

Correct answerYour answer

1 + v + v^{2}

Correct answerYour answer

1 + 2v + v^{2}

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer C

Correct answer: C

Worth noting

$1 + v^{2}$ is what is left after the $v$ cancels in the next step, not $F$ itself.

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

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