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Example 10 - Find general solution: dy/dx = 1+y2 / 1+x2 - Variable separation - Equation given

  1. Chapter 9 Class 12 Differential Equations
  2. Serial order wise
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Example 10 Find the general solution of the differential equation 𝑑𝑦﷮𝑑𝑥﷯= 1+ 𝑦﷮2﷯﷮1+ 𝑥﷮2﷯﷯ 𝑑𝑦﷮𝑑𝑥﷯= 1 + 𝑦﷮2﷯﷮1 + 𝑥﷮2﷯﷯ 𝑑𝑦﷮1 + 𝑦2﷯= 𝑑𝑥﷮1 + 𝑥﷮2﷯﷯ Integrating both sides ﷮﷮ 𝑑𝑦﷮1 + 𝑦﷮2﷯﷯﷯ = ﷮﷮ 𝑑𝑦﷮1 + 𝑥﷮2﷯﷯﷯ tan−1 y = tan−1 x + c tan−1 x = tan−1 x + c is the general solution of the given equation

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