# 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

Chapter 9 Class 12 Differential Equations

Serial order wise

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Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.