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  1. Chapter 9 Class 12 Differential Equations
  2. Serial order wise

Transcript

Example 2 Verify that the function ๐‘ฆ=๐‘’^(โˆ’3๐‘ฅ) is a solution of the differential equation (๐‘‘^2 ๐‘ฆ)/(๐‘‘๐‘ฅ^2 )+๐‘‘๐‘ฆ/๐‘‘๐‘ฅโˆ’6๐‘ฆ=0 ๐‘ฆ=๐‘’^(โˆ’3๐‘ฅ) ๐’…๐’š/๐’…๐’™=๐‘‘(๐‘’^(โˆ’3๐‘ฅ) )/๐‘‘๐‘ฅ ๐‘‘๐‘ฆ/๐‘‘๐‘ฅ=ใ€–โˆ’3 ๐‘’ใ€—^(โˆ’3๐‘ฅ) (๐’…^๐Ÿ ๐’š)/(๐’…๐’™^๐Ÿ )=๐‘‘/๐‘‘๐‘ฅ (๐‘‘๐‘ฆ/๐‘‘๐‘ฅ) =๐‘‘(ใ€–โˆ’3 ๐‘’ใ€—^(โˆ’3๐‘ฅ) )/๐‘‘๐‘ฅ =โˆ’3 ๐‘‘(๐‘’^(โˆ’3๐‘ฅ) )/๐‘‘๐‘ฅ =โˆ’3 ร— (ใ€–โˆ’3 ๐‘’ใ€—^(โˆ’3๐‘ฅ) ) = ใ€–9 ๐‘’ใ€—^(โˆ’3๐‘ฅ) Now, we have to verify (๐‘‘^2 ๐‘ฆ)/(๐‘‘๐‘ฅ^2 )+๐‘‘๐‘ฆ/๐‘‘๐‘ฅโˆ’6๐‘ฆ=0 Solving L.H.S (๐‘‘^2 ๐‘ฆ)/(๐‘‘๐‘ฅ^2 )+๐‘‘๐‘ฆ/๐‘‘๐‘ฅโˆ’6๐‘ฆ Putting values = ใ€–9 ๐‘’ใ€—^(โˆ’3๐‘ฅ)+(โˆ’3๐‘’^(โˆ’3๐‘ฅ) )โˆ’6(๐‘’^(โˆ’3๐‘ฅ) ) =ใ€–9 ๐‘’ใ€—^(โˆ’3๐‘ฅ)โˆ’3๐‘’^(โˆ’3๐‘ฅ)โˆ’6๐‘’^(โˆ’3๐‘ฅ) =ใ€–9 ๐‘’ใ€—^(โˆ’3๐‘ฅ)โˆ’9๐‘’^(โˆ’3๐‘ฅ) =0 = R.H.S โˆด Hence Verified

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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.