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Misc 16 - General solution: y dx - x dy / y = 0 - Class 12 - Miscellaneous

Misc 16 - Chapter 9 Class 12 Differential Equations - Part 2

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Misc 16 The general solution of the differential equation (𝑦 𝑑π‘₯βˆ’π‘₯ 𝑑𝑦)/𝑦=0 is (A) π‘₯𝑦=𝐢 (B) π‘₯=𝐢𝑦^2 (C) 𝑦=𝐢π‘₯ (D) 𝑦=𝐢π‘₯^2 (𝑦 𝑑π‘₯ βˆ’ π‘₯ 𝑑𝑦)/𝑦=0 ( 𝑦 𝑑π‘₯)/π‘¦βˆ’ ( π‘₯ 𝑑𝑦)/𝑦=0 dx = (π‘₯ 𝑑π‘₯)/𝑦 𝑑π‘₯/π‘₯ = 𝑑𝑦/𝑦 Integrating both sides. ∫1β–’γ€–(𝑑π‘₯ )/π‘₯=(𝑑𝑦 )/(𝑦 )γ€— log x = log y + log c1 log x βˆ’ log y = log c1 log ((π‘₯ )/𝑦) = log c1 (π‘₯ )/𝑦 = c1 y = π‘₯/𝑐_1 y = cx ∴ Option (C) is the correct answer

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.