# Ex 9.6, 13 - Chapter 9 Class 12 Differential Equations

Last updated at Nov. 14, 2019 by Teachoo

Last updated at Nov. 14, 2019 by Teachoo

Transcript

Ex 9.6, 13 For each of the differential equations given in Exercises 13 to 15 , find a particular solution satisfy the given condition : ππ¦/ππ₯+2π¦ tanβ‘γπ₯=sinβ‘γπ₯;π¦=0γ γ when π₯= π/3 ππ¦/ππ₯+2π¦ tanβ‘γπ₯=sinβ‘π₯ γ Differential equation is of the form ππ¦/ππ₯ + Py = Q ππ¦/ππ₯ + 2y tan x = sin x Where P = 2 tan x & Q = sin x Finding Integrating factor IF = π^β«1βγπ ππ₯γ IF = π^β«1βγ2 tanβ‘π₯ ππ₯γ IF = e2 log sec x IF = π^logβ‘sec^2β‘π₯ IF = sec2 x Solution is y (IF) = β«1βγ(πΓπΌπΉ)ππ₯+πγ y (sec2 x) = β«1βγsinβ‘π₯ sec^2β‘π₯ ππ₯+πγ y sec2 x = β«1βγsinβ‘π₯ 1/cos^2β‘π₯ γ dx + C y sec2 x = β«1βγsinβ‘π₯/πππ β‘π₯ Γ1/πππ β‘π₯ γ dx + C y sec2 x = β«1βtanβ‘γπ₯ secβ‘γπ₯ γ γ dx + C y sec2 x = secβ‘"x + C " y = secβ‘γπ₯ γ/sec^2β‘π₯ + π/sec^2β‘π₯ y = cos x + C cos2 x Putting x = π/3 & y = 0 0 = cos π/3 + C cos2 π/3 0 = 1/2 + C (1/2)^2 (β1)/2 = C (1/4) (β4)/2 = C C = β2 Putting value of C in (1) y = cos x + C cos2 x y = cos x β 2 cos2 x

Ex 9.6

Ex 9.6, 1
Important

Ex 9.6, 2

Ex 9.6, 3

Ex 9.6, 4

Ex 9.6, 5

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

Ex 9.6, 13 You are here

Ex 9.6, 14

Ex 9.6, 15

Ex 9.6, 16 Important

Ex 9.6, 17 Important

Ex 9.6, 18

Ex 9.6, 19 Deleted for CBSE Board 2021 Exams only

Chapter 9 Class 12 Differential Equations

Serial order wise

About the Author

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.