Ex 9.5, 18 (MCQ) - Chapter 9 Class 12 Differential Equations

Last updated at April 16, 2024 by

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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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