# Ex 9.6, 19 - Chapter 9 Class 12 Differential Equations

Last updated at May 29, 2018 by Teachoo

Last updated at May 29, 2018 by Teachoo

Transcript

Ex 9.6, 19 The integrating Factor of the differential equation 1− 𝑦2 𝑑𝑥𝑑𝑦+𝑦𝑥=𝑎𝑦 −1<𝑦<1 is (A) 1 𝑦2−1 (B) 1 𝑦2−1 (C) 11− 𝑦2 (D) 1 1− 𝑦2 1− 𝑦2 𝑑𝑦𝑑𝑥+𝑦𝑥=𝑎𝑦 Dividing both sides by 1 − y2 𝑑𝑦𝑑𝑥 + 𝑦𝑥1− 𝑦2 = 𝑎𝑦1− 𝑦2 Differential equation is of the form 𝑑𝑦𝑑𝑥 + P1x = Q1 where P1 = 𝑦1 − 𝑦2 & Q1 = 𝑎𝑦1 − 𝑦2 IF = 𝑒 𝑝1𝑑𝑥 Finding 𝑷𝟏 𝒅𝒚 𝑃1 𝑑𝑦= 𝑦1− 𝑦2 𝑑𝑦 Putting 1 − y2 = t −2y dy = dt y dy = −12 dt ∴ Our equation becomes 𝑃1 𝑑𝑦= −12 𝑑𝑡𝑡 𝑃1 𝑑𝑦= −12 log𝑡 Putting back value of t 𝑃1 𝑑𝑦= −12 log(1− 𝑦2) 𝑃1 𝑑𝑦= log 1− 𝑦2 −12 𝑃1 𝑑𝑦= log 1 1 − 𝑦2 Thus, IF = 𝑒 𝑝1𝑑𝑥 IF = elog 1 1 − 𝑦2 IF = 1 1 − 𝑦2 ∴ Part (D) is correct answer.

Chapter 9 Class 12 Differential Equations

Serial order wise

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Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.