# Ex 9.3, 2 - Chapter 9 Class 12 Differential Equations

Last updated at May 29, 2018 by Teachoo

Last updated at May 29, 2018 by Teachoo

Transcript

Ex 9.3, 2 Form a differential equation representing the given family of curves by eliminating arbitrary constants 𝑎 and 𝑏. 𝑦2=𝑎 𝑏2− 𝑥2 𝑦2=𝑎 𝑏2− 𝑥2 𝑦2=𝑎 𝑏2−𝑎 𝑥2 Here, We Eliminate Constant By Differentiating 𝑦 ∴ Diff. Both Sides w.r.t. 𝑥 2𝑦. 𝑑𝑦𝑑𝑥=0−2𝑎𝑥 2𝑦 𝑑𝑦𝑑𝑥=−2𝑎𝑥 𝑦 𝑑𝑦𝑑𝑥=−𝑎𝑥 − 𝑦𝑥 𝑑𝑦𝑑𝑥 = 𝑎 𝑎 = −𝑦𝑥 𝑑𝑦𝑑𝑥 Now, 𝑦 𝑑𝑦𝑑𝑥=−𝑎𝑥 Again Differentiating w.r.t. 𝑥 𝑑𝑦𝑑𝑥. 𝑑𝑦𝑑𝑥+𝑦. 𝑑𝑑𝑥 𝑑𝑦𝑑𝑥=−𝑎 𝑑𝑥𝑑𝑥 𝑑𝑦𝑑𝑥2+𝑦. 𝑑2𝑦𝑑 𝑥2=−𝑎 𝑑𝑦𝑑𝑥2+𝑦. 𝑑2𝑦𝑑 𝑥2= 𝑦𝑥 𝑑𝑦𝑑𝑥 𝑦′2+𝑦. 𝑦′′= 𝑦𝑥. 𝑦′ 𝑥 𝑦′2+𝑥𝑦 𝑦′′=𝑦. 𝑦′ 𝒙𝒚 𝒚′′+𝒙 𝒚′𝟐−𝒚. 𝒚′=𝟎 which is the required differential equation

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Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.