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Ex 9.3, 7 - Chapter 9 Class 12 Differential Equations

Last updated at May 29, 2023 by

Ex 9.4, 7 - Find general solution: y log y dx - x dy = 0

Ex 9.4, 7 - Chapter 9 Class 12 Differential Equations - Part 2
Ex 9.4, 7 - Chapter 9 Class 12 Differential Equations - Part 3

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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‘ฅ/๐‘ฅ = ๐‘‘๐‘ฆ/(๐‘ฆ logโก๐‘ฆ ) Integrating both sides โˆซ1โ–’ใ€–๐‘‘๐‘ฆ/(๐‘ฆ logโก๐‘ฆ )= โˆซ1โ–’๐‘‘๐‘ฅ/๐‘ฅใ€— โˆซ1โ–’๐‘‘๐‘ฆ/(๐‘ฆ logโก๐‘ฆ )=logโกใ€–|๐‘ฅ|ใ€—+๐ถ 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‘œ๐‘” |๐‘ก|=๐‘™๐‘œ๐‘”โก|๐‘ฅ|+logโก๐ถ 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

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.