# Ex 9.5, 13 - Chapter 9 Class 12 Differential Equations

Last updated at April 16, 2024 by Teachoo

Ex 9.5

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Ex 9.5, 2

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Ex 9.5, 13 You are here

Ex 9.5, 14 Important

Ex 9.5, 15

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Ex 9.5, 17 Important

Ex 9.5, 18 (MCQ)

Ex 9.5, 19 (MCQ) Important

Last updated at April 16, 2024 by Teachoo

Ex 9.5, 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 π π/π π + 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«1βγπππβ‘π γπππγ^πβ‘π π π+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 /π & 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