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Question 15 - CBSE Class 12 Sample Paper for 2023 Boards - Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

Last updated at April 16, 2024 by

The general solution of the differential equation 𝑦𝑑π‘₯ − π‘₯𝑑𝑦 = 0 𝑖𝑠

(a) π‘₯𝑦 = 𝐢  

(b) π‘₯ = Cy 2  

(c) 𝑦 = 𝐢π‘₯  

(d) 𝑦 = Cx 2

 

This question is Similar to Misc-16 - Class-12 Miscellaneous

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Transcript

Question 15 The general solution of the differential equation 𝑦𝑑π‘₯ βˆ’ π‘₯𝑑𝑦 = 0 𝑖𝑠 (a) π‘₯𝑦 = 𝐢 (b) π‘₯ = 〖𝐢𝑦〗^2 (c) 𝑦 = 𝐢π‘₯ (d) 𝑦 = Cπ‘₯^2𝑦 𝑑π‘₯ βˆ’ π‘₯ 𝑑𝑦=0 𝑦 𝑑π‘₯= π‘₯ 𝑑𝑦 𝒅𝒙/𝒙 = π’…π’š/π’š Integrating both sides. ∫1β–’γ€–(𝑑π‘₯ )/π‘₯=(𝑑𝑦 )/(𝑦 )γ€— log x = log y + C log x βˆ’ log y = C log ((𝒙 )/π’š) = C (𝒙 )/π’š = c1 y = π‘₯/𝑐_1 y = Cx So, the correct answer is (c)

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