What is the integrating factor of ydx/dy - x = 2y^3?

Homogeneous & Linear Differential Equations · Question 73 of 120

Question 73

MediumOriginal question

What is the integrating factor of $y\frac{dx}{dy} - x = 2y^{3}$ ?

y

Correct answerYour answer

\frac{1}{x}

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e^{-y}

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\frac{1}{y}

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Show the answer and explanation

CorrectNot quiteAnswer D

Correct answer: D

Divide by $y$ : $\frac{dx}{dy} - \frac{1}{y}x = 2y^{2}$ , linear in $x$ with $P = -\frac{1}{y}$ .
$e^{-\int \frac{dy}{y}} = e^{-\log y} = \frac{1}{y}$ .

Worth noting

$y$ is the factor for $+\frac{x}{y}$ ; the minus sign turns it into $\frac{1}{y}$ .

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

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