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Ex 9.6
Ex 9.6, 2
Ex 9.6, 3 Important
Ex 9.6, 4
Ex 9.6, 5 Important You are here
Ex 9.6, 6
Ex 9.6, 7 Important
Ex 9.6, 8 Important
Ex 9.6, 9
Ex 9.6, 10
Ex 9.6, 11
Ex 9.6, 12 Important
Ex 9.6, 13
Ex 9.6, 14 Important
Ex 9.6, 15
Ex 9.6, 16 Important
Ex 9.6, 17 Important
Ex 9.6, 18 (MCQ)
Ex 9.6, 19 (MCQ) Important
Last updated at March 16, 2023 by Teachoo
Ex 9.6, 5 For each of the differential equation given in Exercises 1 to 12, find the general solution : cos2𝑥 𝑑𝑦𝑑𝑥+𝑦=𝑡𝑎𝑛𝑥 0≤𝑥< 𝜋2 Step 1: Put in form 𝑑𝑦𝑑𝑥 + Py = Q cos2x. 𝑑𝑦𝑑𝑥 + y = tan x Dividing by cos2x, 𝑑𝑦𝑑𝑥 + y. 1𝑐𝑜𝑠2𝑥 = tan𝑥𝑐𝑜𝑠2𝑥 ⇒ 𝑑𝑦𝑑𝑥 + (sec2x)y = sec2x. tan x Step 2: Find P and Q Comparing (1) with 𝑑𝑦𝑑𝑥 + Py = Q P = sec2 x and Q = sec2 x. tan x Step 3 : Find integrating factor, I.F I.F = e 𝑝𝑑𝑥 I.F = e 𝑠𝑒𝑐2𝑥.𝑑𝑥 I.F. = etan x Step 4 : Solution of the equation y × I.F. = 𝑄×𝐼.𝐹.𝑑𝑥+𝑐 Putting values, y.etan x = 𝑠𝑒𝑐2𝑥. tan𝑥.etan x.dx + C Let I = 𝑠𝑒𝑐2𝑥. tan𝑥.etan x.dx Putting t = tan x ⇒ 𝑠𝑒𝑐2𝑥.dx = dt Putting values of t & dt in equation ∴ I = tan𝑥.etan x.(𝑠𝑒𝑐2𝑥.𝑑𝑥) I = 𝑡. 𝑒𝑡.𝑑𝑡 I = t 𝑒𝑡𝑑𝑡 − 𝑑𝑡𝑑𝑡 𝑒𝑡𝑑𝑡𝑑𝑡 I = t.et − et 𝑑𝑡 I = 𝑡et − et . Putting t = tan x I = tan x. etan x – etan x I = etan x ( tan x − 1) Substituting value of I in (2), y etan x = etan x (tan x − 1) + C Dividing by etan x, y = tan x − 1 + C. e–tan x