Ex 9.4, 2 - Find general solution: dy/dx = root 4 - y2 - Variable separation - Equation given

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  1. Chapter 9 Class 12 Differential Equations
  2. Serial order wise
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Ex 9.4, 2 For each of the differential equations in Exercises 1 to 10, find the general solution : 𝑑𝑦﷮𝑑𝑥﷯= ﷮4− 𝑦﷮2﷯﷯ −2<𝑦<2﷯ 𝑑𝑦﷮𝑑𝑥﷯ = ﷮4−𝑦2﷯ 𝑑𝑦﷮ ﷮4 − 𝑦2﷯﷯ = dx. 𝑑𝑦﷮ ﷮22−𝑦2﷯﷯ = dx Integrating both sides ﷮﷮ 𝑑𝑦﷮ ﷮ 2﷮2﷯ − 𝑦﷮2﷯﷯﷯= ﷮﷮𝑑𝑥﷯﷯ sin﷮−1﷯﷮ 𝑦﷮2﷯﷯ = x + c 𝑦﷮2﷯ = sin(x + c) y = 2 sin(x + c) ∴ y = 2 sin (x + c) is the general solution

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