Ex 9.2, 4 - Chapter 9 Class 12 Differential Equations

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

Ex 9.2, 4 - Chapter 9 Class 12 Differential Equations - Part 2

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Ex 9.2, 4 Verify that the given functions (explicit or implicit) is a solution of the corresponding differential equation : š‘¦=āˆš(1+š‘„^2 ) : š‘¦^ā€²=š‘„š‘¦/(1+š‘„^2 ) š‘¦=āˆš(1+š‘„^2 ) š‘‘š‘¦/š‘‘š‘„=š‘‘(āˆš(1 + š‘„^2 ))/š‘‘š‘„ =1/(2āˆš(1 + š‘„^2 ))Ɨ2š‘„ =š‘„/āˆš(1 + š‘„^2 ) Now, we have to verify š‘¦^ā€²=š‘„š‘¦/(1 + š‘„^2 ) Taking L.H.S š‘¦^ā€² = š‘„/āˆš(1 + š‘„^2 ) =š‘„/(āˆš(1 + š‘„^2 ) ) Ɨ š‘¦/š‘¦ =š‘„š‘¦/(āˆš(1 + š‘„^2 ) Ɨ āˆš(1 + š‘„2)) =š‘„š‘¦/(1 + š‘„^2 ) = R.H.S Hence Verified (Multiplying and dividing by y) (š‘ˆš‘ š‘–š‘›š‘” š‘¦=āˆš(1āˆ’š‘„^2 ) š‘–š‘› denominator )

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