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Homogeneous & Linear Differential Equations · Question 70 of 120

Question 70

MediumOriginal question

What is the integrating factor of dydx−ytan⁡x=sin⁡x\frac{dy}{dx} - y\tan x = \sin x?

Options for question 70

Show the answer and explanation
CorrectNot quiteAnswer B

Correct answer: B

Explanation

  1. In the form dydx+Py=Q\frac{dy}{dx} + Py = Q, P=−tan⁡xP = - \tan x.

  2. The factor is e∫P dx=cos⁡xe^{\int P\,dx} = \cos x.

Worth noting

sec⁡x\sec x is the factor for +ytan⁡x+y\tan x; with the minus sign, ∫−tan⁡x dx=log⁡cos⁡x\int -\tan x\,dx = \log \cos x.

Concept
The integrating factor
Typical time
90 s
Your time
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The rule this testsLinear equations and the integrating factor
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Ten questions from Homogeneous & Linear Differential Equations, at your own pace.

Practise this chapter →

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