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

Ex 9.4, 2 - Chapter 9 Class 12 Differential Equations - Part 2

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Transcript

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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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.