# Misc 3 - Chapter 9 Class 12 Differential Equations

Last updated at May 29, 2018 by Teachoo

Last updated at May 29, 2018 by Teachoo

Transcript

Misc 3 From the differential equation representing the family of curves given by 𝑥−𝑎2+2 𝑦2= 𝑎2, where 𝑎 is an arbitrary constant Number of time we Differentiate is equal to number of constants. 𝑥−𝑎2+2 𝑦2= 𝑎2 Differentiating w.r.t. 𝑥 Both Sides 𝑑 𝑥 − 𝑎2 + 2 𝑦2𝑑𝑥= 𝑑( 𝑎2)𝑑𝑥 2 𝑥−𝑎+2.2𝑦 𝑑𝑦𝑑𝑥=0 4𝑦 𝑑𝑦𝑑𝑥=−2 𝑥−𝑎 2𝑦 𝑑𝑦𝑑𝑥=− 𝑥−𝑎 2𝑦 𝑑𝑦𝑑𝑥=𝑎−𝑥 a = 2𝑦 𝑑𝑦𝑑𝑥+𝑥 Putting Value of in 𝑥−𝑎2+2 𝑦2= 𝑎2 𝑥− 2𝑦 𝑑𝑦𝑑𝑥+𝑥2+2 𝑦2= 2𝑦 𝑑𝑦𝑑𝑥+𝑥2 𝑥−𝑥−2𝑦 𝑑𝑦𝑑𝑥2+2 y2= 2𝑦 𝑑𝑦𝑑𝑥+𝑥2 −2𝑦 𝑑𝑦𝑑𝑥2+2 𝑦2= 2𝑦 𝑑𝑦𝑑𝑥2+ 𝑥2+2 . 2𝑦 𝑑𝑦𝑑𝑥 . 𝑥 2𝑦 𝑑𝑦𝑑𝑥2− 2𝑦 𝑑𝑦𝑑𝑥2+2 𝑦2= 𝑥2+2𝑥 . 2𝑦 𝑑𝑦𝑑𝑥 2 𝑦2− 𝑥2=4𝑥𝑦 𝑑𝑦𝑑𝑥 2 𝑦2− 𝑥24𝑥𝑦= 𝑑𝑦𝑑𝑥 𝑑𝑦𝑑𝑥= 2 𝑦2 − 𝑥24𝑥𝑦 𝒚′= 𝟐 𝒚𝟐 − 𝒙𝟐𝟒𝒙𝒚

Chapter 9 Class 12 Differential Equations

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 9 years. He provides courses for Maths and Science at Teachoo.