Ex 9.3

Chapter 9 Class 12 Differential Equations
Serial order wise

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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 โ๐ฅ ๐๐ฆ=0ใ ๐ฆ logโกใ๐ฆ ๐๐ฅ โ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 โซ1โใ๐๐ฆ/(๐ฆ logโก๐ฆ )= โซ1โ๐๐ฅ/๐ฅใ โซ1โ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 โซ1โ(๐ฆ ๐๐ก)/(๐ฆ.๐ก)=logโกใ|๐ฅ|ใ+๐ถ โซ1โ๐๐ก/๐ก=logโกใ|๐ฅ|ใ+๐ถ ๐๐๐ |๐ก|=๐๐๐โกใ|๐ฅ|ใ+๐ถ ๐๐๐ |๐ก|=๐๐๐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 + log b) Cancelling log log y = cx y = ecx