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

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  1. Chapter 9 Class 12 Differential Equations
  2. Serial order wise
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Ex 9.4, 7 For each of the differential equations in Exercises 1 to 10, find the general solution : 𝑦 log﷮𝑦 𝑑𝑥 −𝑥 𝑑𝑦=0﷯ y log y dx − x dy = 0 y log y dx = x dy 𝑑𝑥﷮𝑥﷯ = 𝑑𝑦﷮𝑦 log﷮𝑦﷯﷯ Integrating both sides ﷮﷮ 𝑑𝑦﷮𝑦 log﷮𝑦﷯﷯= ﷮﷮ 𝑑𝑥﷮𝑥﷯﷯﷯ Put t = log y dt = 1﷮𝑦﷯ dy dy = y dt Hence, our equation becomes ﷮﷮ 𝑦 𝑑𝑡﷮𝑦.𝑡﷯= ﷮﷮ 𝑑𝑥﷮𝑥﷯﷯﷯ ﷮﷮ 𝑑𝑡﷮𝑡﷯= ﷮﷮ 𝑑𝑥﷮𝑥﷯﷯﷯ log 𝑡﷯ = log 𝑥﷯ + log c Putting t = log y log (log y) = log x + log c log (log y) = log cx log y = cx y = ecx

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