What is the integrating factor of cos xdy/dx + y = 1, for 0 < x < π/2?

Homogeneous & Linear Differential Equations · Question 82 of 120

Question 82

MediumOriginal question

What is the integrating factor of $\cos x\frac{dy}{dx} + y = 1$ , for $0 < x < \frac{\pi}{2}$ ?

\sec x + \tan x

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\sec x

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e^{\sec x}

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e^{\tan x}

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CorrectNot quiteAnswer A

Correct answer: A

Divide by $\cos x$ : $\frac{dy}{dx} + y\sec x = \sec x$ , so $P = \sec x$ .
$\int \sec x\,dx = \log(\sec x + \tan x)$ , so the factor is $\sec x + \tan x$ .

Worth noting

$\sec x$ is $P$ itself, not $e^{\int P\,dx}$ .

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

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