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Last updated at Dec. 10, 2019 by Teachoo
Transcript
Ex 9.2, 4 Verify that the given functions (explicit or implicit) is a solution of the corresponding differential equation : ๐ฆ=โ(1+๐ฅ^2 ) : ๐ฆ^โฒ=๐ฅ๐ฆ/(1+๐ฅ^2 ) ๐ฆ=โ(1+๐ฅ^2 ) ๐๐ฆ/๐๐ฅ=๐(โ(1 + ๐ฅ^2 ))/๐๐ฅ =1/(2โ(1 + ๐ฅ^2 ))ร2๐ฅ =๐ฅ/โ(1 + ๐ฅ^2 ) Now, we have to verify ๐ฆ^โฒ=๐ฅ๐ฆ/(1 + ๐ฅ^2 ) Taking L.H.S ๐ฆ^โฒ = ๐ฅ/โ(1 + ๐ฅ^2 ) =๐ฅ/(โ(1 + ๐ฅ^2 ) ) ร ๐ฆ/๐ฆ =๐ฅ๐ฆ/(โ(1 + ๐ฅ^2 ) ร โ(1 + ๐ฅ2)) =๐ฅ๐ฆ/(1 + ๐ฅ^2 ) = R.H.S Hence Verified (Multiplying and dividing by y) (๐๐ ๐๐๐ ๐ฆ=โ(1โ๐ฅ^2 ) ๐๐ denominator )
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