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Ex 9.5, 18 The integrating Factor of the differential equation ๐‘ฅ ๐‘‘๐‘ฆ/๐‘‘๐‘ฅโˆ’๐‘ฆ=2๐‘ฅ^2 is (A) ๐‘’^(โˆ’๐‘ฅ) (B) ๐‘’^(โˆ’๐‘ฆ) (C) 1/๐‘ฅ (D) ๐‘ฅ ๐‘ฅ ๐‘‘๐‘ฆ/๐‘‘๐‘ฅโˆ’๐‘ฆ=2๐‘ฅ^2 Dividing both sides by x ๐’…๐’š/๐’…๐’™ โˆ’ ๐’š/๐’™ = 2x Differential equation in of the form ๐‘‘๐‘ฆ/๐‘‘๐‘ฅ + ๐‘ƒ๐‘ฆ = Q where P = (โˆ’๐Ÿ)/๐’™ & Q = 2x IF = ๐‘’^โˆซ1โ–’ใ€–๐‘ ๐‘‘๐‘ฅใ€— IF = ๐ž^(โˆซ1โ–’(โˆ’๐Ÿ)/๐’™ ๐’…๐’™) IF = ๐‘’^("โˆ’" logโก๐‘ฅ ) IF = ๐‘’^logโกใ€–๐‘ฅ^(โˆ’1) ใ€— IF = xโˆ’1 IF = ๐Ÿ/๐’™ So, the correct answer is (c)

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.