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Example 9 - Find general solution of dy/dx = x+1 / 2-y - Variable separation - Equation given

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  1. Chapter 9 Class 12 Differential Equations
  2. Serial order wise
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Example 9 Find the general solution of the differential equation 𝑑𝑦﷮𝑑𝑥﷯= 𝑥+1﷮2−𝑦﷯ , 𝑦≠2﷯ 𝑑𝑦﷮𝑑𝑥﷯= 𝑥 + 1﷮2 − 𝑦﷯ , 𝑦≠2﷯ (2 − y) dy = (x + 1) dx Integrating both sides. ﷮﷮ 2−𝑦﷯𝑑𝑦=﷯ ﷮﷮ 𝑥+1﷯𝑑𝑥﷯ 2y − 𝑦﷮2﷯﷮2﷯ = 𝑥﷮2﷯﷮2﷯ + x + c 4𝑦 − 𝑦﷮2﷯﷮2﷯ = 𝑥﷮2﷯+ 2𝑥 + 2𝑐﷮2﷯ 4y − y2 = x2 + 2x + 2c 4y − y2 = x2 − 2x + r x2 + y2 − 2x − 4y + r = 0 is general solution

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