EduFarming
Your list · 0हिं

Type at least two letters. Press Esc to close.

↑↓ navigate↵ openTAB cycle filter

Homogeneous & Linear Differential Equations · Question 74 of 120

Question 74

MediumOriginal question

What is the integrating factor of dydx+ycot⁡x=2cos⁡x\frac{dy}{dx} + y\cot x = 2\cos x?

Options for question 74

Show the answer and explanation
CorrectNot quiteAnswer A

Correct answer: A

Explanation

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

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

Worth noting

log⁡sin⁡x\log \sin x is ∫cot⁡x dx\int \cot x\,dx; the factor is ee raised to it.

Concept
The integrating factor
Typical time
90 s
Your time
—
The rule this testsLinear equations and the integrating factor
Practise this chapter →

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.