# Ex 9.3, 8 - Chapter 9 Class 12 Differential Equations (Term 2)

Last updated at Dec. 10, 2019 by Teachoo

Ex 9.3

Ex 9.3, 1
Deleted for CBSE Board 2023 Exams

Ex 9.3, 2 Deleted for CBSE Board 2023 Exams

Ex 9.3, 3 Important Deleted for CBSE Board 2023 Exams

Ex 9.3, 4 Deleted for CBSE Board 2023 Exams

Ex 9.3, 5 Important Deleted for CBSE Board 2023 Exams

Ex 9.3, 6 Deleted for CBSE Board 2023 Exams

Ex 9.3, 7 Important Deleted for CBSE Board 2023 Exams

Ex 9.3, 8 Deleted for CBSE Board 2023 Exams You are here

Ex 9.3, 9 Deleted for CBSE Board 2023 Exams

Ex 9.3, 10 Important Deleted for CBSE Board 2023 Exams

Ex 9.3, 11 (MCQ) Deleted for CBSE Board 2023 Exams

Ex 9.3, 12 (MCQ) Important Deleted for CBSE Board 2023 Exams

Chapter 9 Class 12 Differential Equations

Serial order wise

Last updated at Dec. 10, 2019 by Teachoo

Ex 9.3, 8 Form the differential equation of the family of ellipses having foci on 𝑦−𝑎𝑥𝑖𝑠 and center at origin. Equation of ellipse having center at origin (0, 0) & foci on y-axis is 𝑥^2/𝑏^2 +𝑦^2/𝑎^2 =1 ∴ Differentiating Both Sides w.r.t. 𝑥 𝑑/𝑑𝑥 [𝑥^2/𝑏^2 +𝑦^2/𝑎^2 ] = (𝑑(1))/𝑑𝑥 1/𝑏^2 [2𝑥]+1/𝑎^2 [2𝑦] 𝑑𝑦/𝑑𝑥=0 2𝑥/𝑏^2 +2𝑦/𝑎^2 . 𝑑𝑦/𝑑𝑥=0 Since it has two variables, we will differentiate twice 2𝑦/𝑎^2 𝑦′=(−2𝑥)/𝑏^2 𝑦/𝑎^2 𝑦′=(−𝑥)/𝑏^2 (𝑦/𝑥)𝑦′=(−𝑎^2)/〖 𝑏〗^2 (𝑦𝑦^′)/𝑥 = (−𝑎^2)/𝑏^2 Again differentiating both sides w.r.t. x ((𝑦𝑦^′ )^′ 𝑥 − (𝑑𝑥/𝑑𝑥)(𝑦𝑦^′ ))/𝑥^2 =0 (𝑦𝑦^′ )^′ 𝑥 − (1)(𝑦𝑦^′ )=𝟎×𝒙^𝟐 (𝑦𝑦^′ )^′ 𝑥 −𝑦𝑦^′=𝟎 (Using Quotient rule and Diff. of constant is 0) (𝒚𝒚^′ )^′ 𝑥 −𝑦𝑦^′=0 (𝒚^′ 𝒚^′+𝒚𝒚′′)𝑥 −𝑦𝑦^′=0 (〖𝑦^′〗^2+𝑦𝑦′′)𝑥 −𝑦𝑦^′=0 𝑥〖𝑦^′〗^2+𝑥𝑦𝑦^′′−𝑦𝑦^′=0 𝒙𝒚𝒚^′′+𝒙〖𝒚^′〗^𝟐−𝒚𝒚^′=𝟎 (Using Product rule)