Ex 9.3, 13 - Chapter 9 Class 12 Differential Equations

Last updated at Dec. 16, 2024 by

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Ex 9.3, 13 For each of the differential equations in Exercises 11 to 14, find a particular solution satisfying the given condition : ๐‘๐‘œ๐‘ (๐‘‘๐‘ฆ/๐‘‘๐‘ฅ)=๐‘Ž(๐‘Žโˆˆ๐‘);๐‘ฆ=2 When ๐‘ฅ=0 cos (๐‘‘๐‘ฆ/๐‘‘๐‘ฅ) = ๐‘Ž ๐‘‘๐‘ฆ/๐‘‘๐‘ฅ = cosโˆ’1 ๐‘Ž ๐’…y = cosโˆ’1 ๐‘Ž dx Integrating both sides โˆซ1โ–’ใ€–๐‘‘๐‘ฆ=ใ€— โˆซ1โ–’ใ€–cos^(โˆ’1)โกใ€–๐‘Ž ๐‘‘๐‘ฅใ€— ใ€— y = x ใ€–๐’„๐’๐’”ใ€—^(โˆ’๐Ÿ) ๐‘Ž + c Putting x = 0 and y = 2 2 = 0 cos^(โˆ’1) ๐‘Ž + c 2 = c c = 2 Putting value of c in (1) y = x cos^(โˆ’1) ๐‘Ž + 2 y โˆ’ 2 = x ใ€–๐’„๐’๐’”ใ€—^(โˆ’๐Ÿ) ๐‘Ž (๐‘ฆ โˆ’ 2)/๐‘ฅ = cos^(โˆ’1) ๐‘Ž cos ((๐’š โˆ’ ๐Ÿ)/๐’™)= ๐‘Ž

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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 and Computer Science at Teachoo