1. Chapter 9 Class 12 Differential Equations
  2. Serial order wise


Misc 3 From the differential equation representing the family of curves given by (๐‘ฅโˆ’๐‘Ž)^2+2๐‘ฆ^2=๐‘Ž^2, where ๐‘Ž is an arbitrary constant (๐‘ฅโˆ’๐‘Ž)^2+2๐‘ฆ^2=๐‘Ž^2 Differentiating w.r.t. ๐‘ฅ ใ€–[(๐‘ฅโˆ’๐‘Ž)^2]ใ€—^โ€ฒ+(2๐‘ฆ^2 )^โ€ฒ=(๐‘Ž^2 )^โ€ฒ 2(๐‘ฅโˆ’๐‘Ž)+2ร—2๐‘ฆ๐‘ฆ^โ€ฒ=0 (๐‘ฅโˆ’๐‘Ž)+2๐‘ฆ๐‘ฆ^โ€ฒ=0 ๐‘ฅ+2๐‘ฆ๐‘ฆ^โ€ฒ=๐‘Ž ๐‘Ž=๐‘ฅ+2ใ€–๐‘ฆ๐‘ฆใ€—^โ€ฒ Since it has one variable, we will differentiate once a = 2๐‘ฆ ๐‘‘๐‘ฆ/๐‘‘๐‘ฅ+๐‘ฅ Putting value of a in (๐‘ฅโˆ’๐‘Ž)^2+2๐‘ฆ^2=๐‘Ž^2 [๐‘ฅโˆ’(๐‘ฅ+2๐‘ฆ๐‘ฆ^โ€ฒ)]^2+2๐‘ฆ^2=ใ€–(๐‘ฅ+2๐‘ฆ๐‘ฆ^โ€ฒ)ใ€—^2 (โˆ’2๐‘ฆ๐‘ฆ^โ€ฒ )^2+2๐‘ฆ^2=ใ€–(๐‘ฅ+2๐‘ฆ๐‘ฆ^โ€ฒ)ใ€—^2 4๐‘ฆ^2 ใ€–๐‘ฆ^โ€ฒใ€—^2+2๐‘ฆ^2=๐‘ฅ^2+4๐‘ฆ^2 ใ€–๐‘ฆ^โ€ฒใ€—^2+4๐‘ฅ๐‘ฆ๐‘ฆ^โ€ฒ 2๐‘ฆ^2=๐‘ฅ^2+4๐‘ฅ๐‘ฆ๐‘ฆ^โ€ฒ 2๐‘ฆ^2โˆ’๐‘ฅ^2=4๐‘ฅ๐‘ฆ๐‘ฆ^โ€ฒ (2๐‘ฆ^2โˆ’ ๐‘ฅ^2)/4๐‘ฅ๐‘ฆ=๐‘ฆ^โ€ฒ ๐’š^โ€ฒ=(๐Ÿ๐’š^๐Ÿ โˆ’ ๐’™^๐Ÿ)/๐Ÿ’๐’™๐’š

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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.