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Ex 9.2, 10 -  Verify solution y = root a2 - x2 , x + y dy/dx = 0 - 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, 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 : 𝑦= ﷮ 𝑎﷮2﷯− 𝑥﷮2﷯﷯ 𝑥 ∈ −𝑎 , 𝑎﷯ : 𝑥+𝑦 𝑑𝑦﷮𝑑𝑥﷯=0 𝑦≠0﷯ 𝑦= ﷮ 𝑎﷮2﷯− 𝑥﷮2﷯﷯ Differently Both Sides w.r.t 𝑥 𝑑𝑦﷮𝑑𝑥﷯= 𝑑﷮𝑑𝑥﷯ ﷮ 𝑎﷮2﷯− 𝑥﷮2﷯﷯﷯ = 1﷮2 𝑎﷮2﷯ − 𝑥﷮2﷯﷯﷮ 1﷮2﷯﷯﷯ −2𝑥﷯ = −𝑥﷮ ﷮ 𝑎﷮2﷯ − 𝑥﷮2﷯﷯﷯﷯ Now, We Have to Verify 𝑥+𝑦 𝑑𝑦﷮𝑑𝑥﷯=0 Taking LHS 𝑥+𝑦 𝑑𝑦﷮𝑑𝑥﷯=0 =𝑥+𝑦 −𝑥﷮ ﷮ 𝑎﷮2﷯ − 𝑥﷮2﷯﷯﷯﷯ =𝑥+ ﷮ 𝑎﷮2﷯− 𝑥﷮2﷯﷯ −𝑥﷮ ﷮ 𝑎﷮2﷯ − 𝑥﷮2﷯﷯﷯﷯ =𝑥−𝑥 =0 = R.H.S Hence Verified

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