Ex 9.2, 4 - Verify solution: y = root 1 + x2, y' = xy/1+x2 - Ex 9.2

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  1. Chapter 9 Class 12 Differential Equations
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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‘‘/๐‘‘๐‘ฅ (โˆš(1+๐‘ฅ^2 ))=1/(2(1 + ๐‘ฅ^2 )" " ^(1/2) ) [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 โˆš(1 + ๐‘ฅ2)) ) =๐‘ฅ๐‘ฆ/(1 + ๐‘ฅ^2 ) = R.H.S Hence Verified

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