1. Chapter 9 Class 12 Differential Equations
  2. Serial order wise
  3. Miscellaneous
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Question 1 - Miscellaneous - Chapter 9 Class 12 Differential Equations

Last updated at Dec. 16, 2024 by Teachoo

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

    3. Miscellaneous

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Chapter 9 Class 12 Differential Equations
Serial order wise

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo