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


Ex 9.2, 10 In each of the Exercises 1 to 10 verify that the given functions (explicit or implicit) is a solution of the corresponding differential equation : ๐‘ฆ=โˆš(๐‘Ž^2โˆ’๐‘ฅ^2 ) ๐‘ฅ โˆˆ (โˆ’๐‘Ž , ๐‘Ž) : ๐‘ฅ+๐‘ฆ ๐‘‘๐‘ฆ/๐‘‘๐‘ฅ=0(๐‘ฆโ‰ 0) ๐‘ฆ=โˆš(๐‘Ž^2โˆ’๐‘ฅ^2 ) Differentiating Both Sides w.r.t ๐‘ฅ ๐‘‘๐‘ฆ/๐‘‘๐‘ฅ=(๐‘‘(โˆš(๐‘Ž^2 โˆ’ ๐‘ฅ^2 )))/๐‘‘๐‘ฅ =1/(2โˆš(๐‘Ž^2 โˆ’ ๐‘ฅ^2 ))ร—(โˆ’2๐‘ฅ) =(โˆ’๐‘ฅ)/โˆš((๐‘Ž^2 โˆ’ ๐‘ฅ^2 ) ) (Using Chain Rule) Now, We Have to Verify ๐‘ฅ+๐‘ฆ ๐‘‘๐‘ฆ/๐‘‘๐‘ฅ=0 Taking LHS ๐‘ฅ+๐‘ฆ ๐‘‘๐‘ฆ/๐‘‘๐‘ฅ =๐‘ฅ+๐‘ฆ[(โˆ’๐‘ฅ)/โˆš(๐‘Ž^2 โˆ’ ๐‘ฅ^2 )] =๐‘ฅ+โˆš(๐‘Ž^2โˆ’๐‘ฅ^2 ) [(โˆ’๐‘ฅ)/โˆš(๐‘Ž^2 โˆ’ ๐‘ฅ^2 )] =๐‘ฅโˆ’๐‘ฅ =0 = R.H.S Hence Verified (โ–ˆ(๐‘ˆ๐‘ ๐‘–๐‘›๐‘” ) ๐‘ฆ=โˆš(๐‘Ž^2โˆ’๐‘ฅ^2 ))

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.