Ex 9.3, 13 - Chapter 9 Class 12 Differential Equations

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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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