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

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  1. Chapter 9 Class 12 Differential Equations
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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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