Ex 9.4, 14 - Find particular solution: dy/dx = y tan x, y = 1 - Variable separation - Equation given

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Ex 9.4, 14 For each of the differential equations in Exercises 11 to 14, find a particular solution satisfying the given condition : 𝑑𝑦﷮𝑑𝑥﷯=𝑦 tan﷮ ﷯𝑥;𝑦=1 When 𝑥=0 𝑑𝑦﷮𝑑𝑥﷯=𝑦 tan﷮ ﷯x 𝑑𝑦﷮𝑦﷯= tan x dx﷮ ﷯ Integrating both sides ﷮﷮ 𝑑𝑦﷮𝑦﷯﷯ = ﷮﷮ tan﷮𝑥 𝑑𝑥﷯﷯ log 𝑦﷯ = log sec﷮𝑥﷯﷯+ log﷮𝑐﷯ log 𝑦﷯ = log (c sec x) y = c sec x Put x = 0 and y = 1 1 = C Sec 0 1 = C Put value of C in (1) y = 1 × sec x y = sec x

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