# Ex 9.3, 5 - Chapter 9 Class 12 Differential Equations (Term 2)

Last updated at Dec. 10, 2019 by Teachoo

Last updated at Dec. 10, 2019 by Teachoo

Transcript

Ex 9.3, 5 Form a differential equation representing the given family of curves by eliminating arbitrary constants π and π. π¦=π^π₯ (π cosβ‘γπ₯+π sinβ‘π₯ γ ) Since it has two variables, we will differentiate twice π¦=π^π₯ (π cosβ‘γπ₯+π sinβ‘π₯ γ ) Differentiating Both Sides w.r.t. π₯ ππ¦/ππ₯=π/ππ₯ [π^π₯ (π cosβ‘π₯+π sinβ‘π₯ )] π¦^β²=π(π^π₯ )/ππ₯.[π cosβ‘π₯+π sinβ‘π₯]+π^π₯ π/ππ₯ [π cosβ‘π₯+π sinβ‘π₯] π¦^β²=π^π₯ [π cosβ‘π₯+π sinβ‘π₯]+π^π₯ [βπ sinβ‘π₯+π cosβ‘π₯] π¦^β²=π¦+π^π₯ [βπ sinβ‘π₯+π cosβ‘π₯] π¦^β²βπ¦=π^π₯ [βπ sinβ‘π₯+π cosβ‘π₯] β¦(1) Again Differentiating both sides w.r.t.x π¦^β²β²βπ¦^β²=π(π^π₯ )/ππ₯ [βπ sinβ‘π₯+π cosβ‘π₯]+π^π₯ π/ππ₯ [βπ sinβ‘π₯+π cosβ‘π₯] π¦^β²β²βπ¦^β²=π^π [βπ πππβ‘π+π πππβ‘π]+π^π₯ [βπ cosβ‘π₯+π (βsinβ‘π₯)] π¦^β²β²βπ¦^β²=γ(πγ^β²β π)+π^π₯ [βπ cosβ‘π₯βπ sinβ‘π₯] π¦^β²β²βπ¦^β²=π¦^β²βπ¦βπ^π [π πππβ‘π+π πππβ‘π] π¦^β²β²βπ¦^β²=π¦^β²βπ¦βπ¦ π¦^β²β²βπ¦^β²=π¦^β²β2π¦ π¦^β²β²βπ¦^β²βπ¦^β²+2π¦=0 π¦^β²β²β2π¦^β²+2π¦=0 which is the required differential equation (From (1)) (Using y = π^π₯ (π cos x + b sin x))

Ex 9.3

Ex 9.3, 1
Deleted for CBSE Board 2022 Exams

Ex 9.3, 2 Deleted for CBSE Board 2022 Exams

Ex 9.3, 3 Important Deleted for CBSE Board 2022 Exams

Ex 9.3, 4 Deleted for CBSE Board 2022 Exams

Ex 9.3, 5 Important Deleted for CBSE Board 2022 Exams You are here

Ex 9.3, 6 Deleted for CBSE Board 2022 Exams

Ex 9.3, 7 Important Deleted for CBSE Board 2022 Exams

Ex 9.3, 8 Deleted for CBSE Board 2022 Exams

Ex 9.3, 9 Deleted for CBSE Board 2022 Exams

Ex 9.3, 10 Important Deleted for CBSE Board 2022 Exams

Ex 9.3, 11 (MCQ) Deleted for CBSE Board 2022 Exams

Ex 9.3, 12 (MCQ) Important Deleted for CBSE Board 2022 Exams

Chapter 9 Class 12 Differential Equations (Term 2)

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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.