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Ex 9.6, 18 - The integrating factor of differential equation - Ex 9.6

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  1. Chapter 9 Class 12 Differential Equations
  2. Serial order wise
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Ex 9.6, 18 The integrating Factor of the differential equation 𝑥 𝑑𝑦﷮𝑑𝑥﷯−𝑦=2 𝑥﷮2﷯ is (A) 𝑒﷮−𝑥﷯ (B) 𝑒﷮−𝑦﷯ (C) 1﷮𝑥﷯ (D) 𝑥 𝑥 𝑑𝑦﷮𝑑𝑥﷯−𝑦=2 𝑥﷮2﷯ Dividing both sides by x 𝑑𝑦﷮𝑑𝑥﷯ − 𝑦﷮𝑥﷯ = 2x Differential equation in of the form 𝑑𝑦﷮𝑑𝑥﷯ + 𝑃𝑦 = Q where P = −1﷮𝑥﷯ & Q = 2x IF = 𝑒﷮ ﷮﷮𝑝 𝑑𝑥﷯﷯ IF = e﷮ ﷮﷮ −1﷮𝑥﷯﷯𝑑𝑥﷯ IF = 𝑒﷮− log﷮𝑥﷯﷯ IF = 𝑒﷮ log﷮ 𝑥﷮−1﷯﷯﷯ IF = x−1 IF = 1﷮𝑥﷯ ∴ Option (C) is correct answer.

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