Ex 9.3, 2 - Chapter 9 Class 12 Differential Equations

Last updated at April 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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