Ex 9.3, 2 - Chapter 9 Class 12 Differential Equations

Last updated at Dec. 16, 2024 by Teachoo

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Ex 9.3, 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 − 𝑦^2 ) = dx. 𝒅𝒚/√(𝟐^𝟐 − 𝒚^𝟐 ) = dx Integrating both sides ∫1▒〖𝑑𝑦/√(2^2 − 𝑦^2 )=∫1▒𝑑𝑥〗 We know that ∫1▒〖𝑑𝑥/√(𝑎^2−𝑥^2 )=sin^(−1)⁡〖𝑥/𝑎〗〗 Putting 𝑎 = 2, x = y 〖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 14 years. He provides courses for Maths, Science and Computer Science at Teachoo

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