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

Last updated at Dec. 11, 2019 by Teachoo

Last updated at Dec. 11, 2019 by Teachoo

Transcript

Ex 9.6, 9 For each of the differential equation find the general solution : π₯ ππ¦/ππ₯+π¦βπ₯+π₯π¦ cotβ‘γπ₯=0(π₯β 0)γ Given equation x ππ¦/ππ₯ + y β x + xy cot x = 0 Dividing both sides by x ππ¦/ππ₯ + π¦/π₯ β 1 + y cot x = 0 ππ¦/ππ₯ + y (1/π₯+cotβ‘π₯ ) β 1 = 0 ππ¦/ππ₯ + (1/π₯+cotβ‘π₯ ) y = 1 β¦(1) Comparing (1) with ππ¦/ππ₯ + Py = Q P = 1/π₯ + cot x & Q = 1 Finding integrating factor, I.F. I.F. = e^β«1βγπ ππ₯ γ = e^β«1β(1/π₯ + cotβ‘π₯ )ππ₯ = e^β«1βγ1/π₯ ππ₯ + β«1βγcotβ‘π₯ ππ₯γγ = π^(logβ‘π₯ + logβ‘sinβ‘π₯ ) = π^logβ‘γ(π₯ sinβ‘π₯)γ = x sin x So, I.F. = x sin x (Using log a + log b = log ab) (Using π^logβ‘π₯ = x) Solution of the equation is y Γ I.F. = β«1βγQΓπΌπΉγβ‘ππ₯ + C y (x sin x) = β«1βγπ₯.γπ ππ π₯γβ‘ππ₯ γ Let I = β«1βγπ₯.sinβ‘γπ₯.ππ₯γ γ I = x β«1βsinβ‘γπ₯ ππ₯ββ«1β[1.β«1βsinβ‘γπ₯ ππ₯γ ]ππ₯γ = x (β cos x) β β«1βγ1.(βcosβ‘γπ₯)γ ππ₯γ = β x. cos x + β«1βcosβ‘γπ₯ ππ₯γ β¦(2) Using formula β«1βγπ(π₯)π(π₯)ππ₯=π(π₯)ππ(π₯)ππ₯ββ«1β[πβ²(π₯)][π(π₯)ππ₯] γ dx Taking f(x) = x & g(x) = sin x = β x cos x + sin x Putting value of I in (2), y x sin x = βx cos x + sin x + C Divide by x sin x y = (βπ₯ cosβ‘π₯)/(π₯ sinβ‘π₯ ) + sinβ‘π₯/(π₯ sinβ‘π₯ ) + πΆ/(π₯ sinβ‘π₯ ) y = βcot x + 1/π₯ + πΆ/(π₯ π ππβ‘π₯ ) y = π/π β cot x + πͺ/(π πππβ‘π ) Which is the general solution of the given differential equation

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

Ex 9.6, 6

Ex 9.6, 7 Important

Ex 9.6, 8 Important

Ex 9.6, 9 You are here

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.