1. Chapter 9 Class 12 Differential Equations
  2. Serial order wise
  3. Ex 9.3
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Ex 9.3, 7 - Chapter 9 Class 12 Differential Equations

Last updated at Dec. 16, 2024 by Teachoo

Transcript

Ex 9.3, 7 For each of the differential equations in Exercises 1 to 10, find the general solution : ๐‘ฆ logโกใ€–๐‘ฆ ๐‘‘๐‘ฅ โˆ’๐‘ฅ ๐‘‘๐‘ฆ=0ใ€— ๐‘ฆ logโกใ€–๐‘ฆ ๐‘‘๐‘ฅ โˆ’๐‘ฅ ๐‘‘๐‘ฆ=0ใ€— ๐‘ฆ logโก๐‘ฆ ๐‘‘๐‘ฅ=๐‘ฅ ๐‘‘๐‘ฆ ๐’…๐’™/๐’™ = ๐’…๐’š/(๐’š ๐ฅ๐จ๐ โก๐’š ) Integrating both sides โˆซ1โ–’ใ€–๐‘‘๐‘ฆ/(๐‘ฆ logโก๐‘ฆ )= โˆซ1โ–’๐‘‘๐‘ฅ/๐‘ฅใ€— โˆซ1โ–’๐’…๐’š/(๐’š ๐’๐’๐’ˆโก๐’š )=๐ฅ๐จ๐ โกใ€–|๐’™|ใ€—+๐‘ช Putting t = log y dt = 1/๐‘ฆ dy dy = y dt Hence, our equation becomes โˆซ1โ–’(๐‘ฆ ๐‘‘๐‘ก)/(๐‘ฆ.๐‘ก)=logโกใ€–|๐‘ฅ|ใ€—+๐ถ โˆซ1โ–’๐‘‘๐‘ก/๐‘ก=logโกใ€–|๐‘ฅ|ใ€—+๐ถ ๐‘™๐‘œ๐‘” |๐‘ก|=๐‘™๐‘œ๐‘”โกใ€–|๐‘ฅ|ใ€—+๐ถ ๐’๐’๐’ˆ |๐’•|=๐’๐’๐’ˆโก|๐’™|+๐ฅ๐จ๐ โก๐‘ช Putting t = log y log (log y) = log x + log c log (log y) = log cx (Using log ab = log ๐‘Ž + log b) Cancelling log log y = cx y = ecx
  1. Chapter 9 Class 12 Differential Equations
  2. Serial order wise

    3. Ex 9.3

    Ex 9.4 →
Ex 9.4 →
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