# Ex 9.6, 5 - Chapter 9 Class 12 Differential Equations (Term 2)

Last updated at Aug. 20, 2021 by Teachoo

Last updated at Aug. 20, 2021 by Teachoo

Transcript

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

Ex 9.6

Ex 9.6, 1
Important

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 Deleted for CBSE Board 2022 Exams

Ex 9.6, 11 Deleted for CBSE Board 2022 Exams

Ex 9.6, 12 Important Deleted for CBSE Board 2022 Exams

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 Deleted for CBSE Board 2022 Exams

Chapter 9 Class 12 Differential Equations (Term 2)

Serial order wise

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Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.