Ex 9.3, 2 - Chapter 9 Class 12 Differential Equations

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Ex 9.3, 2 For each of the differential equations in Exercises 1 to 10, find the general solution : ๐‘‘๐‘ฆ/๐‘‘๐‘ฅ=โˆš(4โˆ’๐‘ฆ^2 ) (โˆ’2<๐‘ฆ<2) ๐‘‘๐‘ฆ/๐‘‘๐‘ฅ = โˆš(4โˆ’๐‘ฆ2) ๐‘‘๐‘ฆ/โˆš(4 โˆ’ ๐‘ฆ^2 ) = dx. ๐’…๐’š/โˆš(๐Ÿ^๐Ÿ โˆ’ ๐’š^๐Ÿ ) = dx Integrating both sides โˆซ1โ–’ใ€–๐‘‘๐‘ฆ/โˆš(2^2 โˆ’ ๐‘ฆ^2 )=โˆซ1โ–’๐‘‘๐‘ฅใ€— We know that โˆซ1โ–’ใ€–๐‘‘๐‘ฅ/โˆš(๐‘Ž^2โˆ’๐‘ฅ^2 )=sin^(โˆ’1)โกใ€–๐‘ฅ/๐‘Žใ€— ใ€— Putting ๐‘Ž = 2, x = y ใ€–๐’”๐’Š๐’ใ€—^(โˆ’๐Ÿ)โกใ€–๐’š/๐Ÿใ€— = x + c ๐‘ฆ/2 = sin(x + c) y = 2 sin(x + c) โˆด y = 2 sin (x + c) is the general solution

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