Ex 9.5, 13 - Chapter 9 Class 12 Differential Equations
Last updated at April 16, 2024 by Teachoo
Solving Linear differential equations - Equation given
Ex 9.5, 19 (MCQ) Important
Misc 14 (MCQ) Important
Ex 9.5, 2
Ex 9.5, 10
Ex 9.5, 3 Important
Ex 9.5, 4
Misc 15 (MCQ)
Ex 9.5, 13 You are here
Ex 9.5, 8 Important
Misc 10 Important
Misc 11
Ex 9.5, 14 Important
Ex 9.5, 6
Ex 9.5, 5 Important
Ex 9.5, 9
Ex 9.5, 7 Important
Ex 9.5, 15
Example 14
Ex 9.5, 1 Important
Ex 9.5, 12 Important
Ex 9.5, 11
Example 16
Example 17 Important
Example 22 Important
Solving Linear differential equations - Equation given
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