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Ex 9.6, 4 - Find general solution: dy/dx + (sec x) y = tan x - Solving Linear differential equations - Equation given

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  1. Chapter 9 Class 12 Differential Equations
  2. Serial order wise
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Ex 9.6, 4 For each of the differential equation given in Exercises 1 to 12, find the general solution : 𝑑𝑦﷮𝑑𝑥﷯+ sec﷮𝑥﷯﷯𝑦=𝑡𝑎𝑛𝑥 0≤𝑥< 𝜋﷮2﷯﷯ Differential equation is of the form 𝑑𝑦﷮𝑑𝑥﷯ + Py = Q where P = sec x and Q = tan x Finding integrating factor, IF = 𝑒﷮ ﷮﷮𝑝 𝑑𝑥﷯﷯ IF = e﷮ ﷮﷮ sec﷮𝑥 𝑑𝑥﷯﷯﷯ IF = e﷮𝑙𝑜𝑔﷯﷮ sec﷮𝑥+ tan﷮𝑥﷯﷯﷯﷯ I.F = sec x + tan x Solution is y (IF) = ﷮﷮ 𝑄×𝐼.𝐹﷯﷯𝑑𝑥+𝑐 y (sec x + tan x) = ﷮﷮ tan﷮𝑥﷯ ( sec﷮𝑥﷯+ tan﷮𝑥)﷯﷯+𝑐 y (sec x + tan x) = ﷮﷮ tan﷮𝑥﷯ sec﷮𝑥﷯﷯ 𝑑𝑥+ ﷮﷮ tan﷮2﷯﷮𝑥﷯𝑑𝑥+𝐶﷯ y (sec x + tan x) = sec x + ﷮﷮( sec﷮2﷯﷮𝑥﷯−1)﷯ dx + c y (sec x + tan x) = sec x + 𝐭𝐚𝐧﷮𝒙﷯ − x + c

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