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Homogeneous & Linear Differential Equations · Question 75 of 120

Question 75

MediumOriginal question

What is the integrating factor of (1+x2)dydx+2xy=1(1 + x^{2})\frac{dy}{dx} + 2xy = 1?

Options for question 75

Show the answer and explanation
CorrectNot quiteAnswer C

Correct answer: C

Explanation

  1. In the form dydx+Py=Q\frac{dy}{dx} + Py = Q, P=2xx2+1P = \frac{2 x}{x^{2} + 1}.

  2. The factor is e∫P dx=x2+1e^{\int P\,dx} = x^{2} + 1.

Worth noting

ex2e^{x^{2}} uses P=2xP = 2x before dividing through by 1+x21 + x^{2}.

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.