

Ex 9.3
Ex 9.3, 2 Deleted for CBSE Board 2022 Exams You are here
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
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
Last updated at Dec. 10, 2019 by Teachoo
Ex 9.3, 2 Form a differential equation representing the given family of curves by eliminating arbitrary constants 𝑎 and 𝑏. 𝑦^2=𝑎(𝑏^2−𝑥^2 ) 𝑦^2=𝑎(𝑏^2−𝑥^2 ) 𝑦^2=𝑎𝑏^2−𝑎𝑥^2 Since it has two variables, we will differentiate twice ∴ Diff. Both Sides w.r.t. 𝑥 2𝑦.𝑑𝑦/𝑑𝑥=0−2𝑎𝑥 2𝑦𝑦^′=−2𝑎𝑥 𝑦𝑦′=−𝑎𝑥 (𝑦𝑦^′)/(−𝑥) = 𝑎 𝑎 = (−𝑦)/𝑥 𝑦′ Now, 𝑦𝑦′=−𝑎𝑥 "Again Differentiating w.r.t. " 𝑥 𝑑𝑦/𝑑𝑥.𝑦^′+𝑦.(𝑑(𝑦^′))/𝑑𝑥=−𝑎 𝑑𝑥/𝑑𝑥 𝑦^′×𝑦^′+𝑦×𝑦^′′=−𝑎 〖𝑦^′〗^2+𝑦𝑦^′′=−((−𝑦)/𝑥 𝑦′) 〖𝑦^′〗^2+𝑦𝑦^′′=(𝑦𝑦^′)/𝑥 𝑥〖𝑦^′〗^2+𝑥𝑦𝑦^′′=𝑦𝑦^′ …(1) ("Using Product Rule ") (From (1) 𝑎= (−𝑦)/𝑥 𝑑𝑦/𝑑𝑥 ) 𝒙𝒚𝒚^′′+𝒙〖𝒚^′〗^𝟐−𝒚𝒚^′=𝟎 which is the required differential equation