Ex 9.3, 7 - Chapter 9 Class 12 Differential Equations

Last updated at Dec. 16, 2024 by Teachoo

Ex 9.3, 7 - Find general solution: y log y dx - x dy = 0 - Ex 9.3

part 2 - Ex 9.3, 7 - Ex 9.3 - Serial order wise - Chapter 9 Class 12 Differential Equations

part 3 - Ex 9.3, 7 - Ex 9.3 - Serial order wise - Chapter 9 Class 12 Differential Equations

Next: Ex 9.3, 8 → Remove Ads

Transcript

Ex 9.3, 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 ∫1▒〖𝑑𝑦/(𝑦 log⁡𝑦 )= ∫1▒𝑑𝑥/𝑥〗 ∫1▒𝒅𝒚/(𝒚 𝒍𝒐𝒈⁡𝒚 )=𝐥𝐨𝐠⁡〖|𝒙|〗+𝑪 Putting t = log y dt = 1/𝑦 dy dy = y dt Hence, our equation becomes ∫1▒(𝑦 𝑑𝑡)/(𝑦.𝑡)=log⁡〖|𝑥|〗+𝐶 ∫1▒𝑑𝑡/𝑡=log⁡〖|𝑥|〗+𝐶 𝑙𝑜𝑔 |𝑡|=𝑙𝑜𝑔⁡〖|𝑥|〗+𝐶 𝒍𝒐𝒈 |𝒕|=𝒍𝒐𝒈⁡|𝒙|+𝐥𝐨𝐠⁡𝑪 Putting t = log y log (log y) = log x + log c log (log y) = log cx (Using log ab = log 𝑎 + log b) Cancelling log log y = cx y = ecx

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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

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