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Slide8.JPG

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

Transcript

Ex 9.2, 4 Verify that the given functions (explicit or implicit) is a solution of the corresponding differential equation : ๐‘ฆ=โˆš(1+๐‘ฅ^2 ) : ๐‘ฆ^โ€ฒ=๐‘ฅ๐‘ฆ/(1+๐‘ฅ^2 ) ๐‘ฆ=โˆš(1+๐‘ฅ^2 ) ๐‘‘๐‘ฆ/๐‘‘๐‘ฅ=๐‘‘(โˆš(1 + ๐‘ฅ^2 ))/๐‘‘๐‘ฅ =1/(2โˆš(1 + ๐‘ฅ^2 ))ร—2๐‘ฅ =๐‘ฅ/โˆš(1 + ๐‘ฅ^2 ) Now, we have to verify ๐‘ฆ^โ€ฒ=๐‘ฅ๐‘ฆ/(1 + ๐‘ฅ^2 ) Taking L.H.S ๐‘ฆ^โ€ฒ = ๐‘ฅ/โˆš(1 + ๐‘ฅ^2 ) =๐‘ฅ/(โˆš(1 + ๐‘ฅ^2 ) ) ร— ๐‘ฆ/๐‘ฆ =๐‘ฅ๐‘ฆ/(โˆš(1 + ๐‘ฅ^2 ) ร— โˆš(1 + ๐‘ฅ2)) =๐‘ฅ๐‘ฆ/(1 + ๐‘ฅ^2 ) = R.H.S Hence Verified (Multiplying and dividing by y) (๐‘ˆ๐‘ ๐‘–๐‘›๐‘” ๐‘ฆ=โˆš(1โˆ’๐‘ฅ^2 ) ๐‘–๐‘› denominator )

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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.