After the substitution, which separated form…

After the substitution, which separated form do you get?

Question 40

MediumOriginal question

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

After the substitution, which separated form do you get?

\frac{dv}{1 + v + v^{2}} = \frac{dx}{x}

Correct answerYour answer

\frac{dv}{1 + v^{2}} = dx

Correct answerYour answer

(1 + v^{2})\,dv = \frac{dx}{x}

Correct answerYour answer

\frac{dv}{1 + v^{2}} = \frac{dx}{x}

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer D

Correct answer: D

Worth noting

$1 + v + v^{2}$ in the denominator forgets to take away the $v$ from $\frac{dy}{dx} = v + x\frac{dv}{dx}$ .

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

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