Ex 9.2, 7 - Verify solution xy = log y + C : y' = y2 / 1 - xy - Ex 9.2

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  1. Chapter 9 Class 12 Differential Equations
  2. Serial order wise
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Ex 9.2, 7 Verify that the given functions (explicit or implicit) is a solution of the corresponding differential equation : 𝑥𝑦= log﷮𝑦+𝐶﷯ : 𝑦﷮′﷯= 𝑦﷮2﷯﷮1−𝑥𝑦﷯ 𝑥𝑦≠1﷯ 𝑥𝑦= log﷮𝑦+𝐶﷯ Differentiating Both Sides w.r.t. 𝑥 𝑑﷮𝑑𝑥﷯ 𝑥𝑦﷯= 𝑑﷮𝑑𝑥﷯ 𝑙𝑜𝑔 𝑦﷯+𝐶﷯ 𝑑 𝑥﷯﷮𝑑𝑥﷯.𝑦+𝑥 𝑑 𝑦﷯﷮𝑑𝑥﷯= 𝑑 log﷮𝑦﷯﷯﷮𝑑𝑥﷯+ 𝑑𝐶﷮𝑑𝑥﷯ 1.𝑦+𝑥 𝑑𝑦﷮𝑑𝑥﷯= 1﷮𝑦﷯. 𝑑𝑦﷮𝑑𝑥﷯+0 𝑦+𝑥 𝑑𝑦﷮𝑑𝑥﷯= 1﷮𝑦﷯. 𝑑𝑦﷮𝑑𝑥﷯ 𝑦= 1﷮𝑦﷯. 𝑑𝑦﷮𝑑𝑥﷯−𝑥. 𝑑𝑦﷮𝑑𝑥﷯ 𝑦= 𝑑𝑦﷮𝑑𝑥﷯ 1﷮𝑦﷯−𝑥﷯ 𝑦= 𝑑𝑦﷮𝑑𝑥﷯ 1 − 𝑥𝑦﷮𝑦﷯﷯ ∴ 𝑑𝑦﷮𝑑𝑥﷯=𝑦. 𝑦﷮1 − 𝑥𝑦﷯ 𝑑𝑦﷮𝑑𝑥﷯ = 𝑦﷮2﷯﷮1 − 𝑥𝑦﷯ ∴ 𝒚﷮′﷯= 𝒚﷮𝟐﷯﷮𝟏 − 𝒙𝒚﷯ Hence Verified

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