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Last updated at Dec. 10, 2019 by Teachoo
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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 : ๐ฆ=โ(๐^2โ๐ฅ^2 ) ๐ฅ โ (โ๐ , ๐) : ๐ฅ+๐ฆ ๐๐ฆ/๐๐ฅ=0(๐ฆโ 0) ๐ฆ=โ(๐^2โ๐ฅ^2 ) Differentiating Both Sides w.r.t ๐ฅ ๐๐ฆ/๐๐ฅ=(๐(โ(๐^2 โ ๐ฅ^2 )))/๐๐ฅ =1/(2โ(๐^2 โ ๐ฅ^2 ))ร(โ2๐ฅ) =(โ๐ฅ)/โ((๐^2 โ ๐ฅ^2 ) ) (Using Chain Rule) Now, We Have to Verify ๐ฅ+๐ฆ ๐๐ฆ/๐๐ฅ=0 Taking LHS ๐ฅ+๐ฆ ๐๐ฆ/๐๐ฅ =๐ฅ+๐ฆ[(โ๐ฅ)/โ(๐^2 โ ๐ฅ^2 )] =๐ฅ+โ(๐^2โ๐ฅ^2 ) [(โ๐ฅ)/โ(๐^2 โ ๐ฅ^2 )] =๐ฅโ๐ฅ =0 = R.H.S Hence Verified (โ(๐๐ ๐๐๐ ) ๐ฆ=โ(๐^2โ๐ฅ^2 ))
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