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Misc 17 - General solution of type dx/dy + p1x = q1 is - Miscellaneous

Misc 17 - Chapter 9 Class 12 Differential Equations - Part 2


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Misc 17 The general solution of a differential equation of the type 𝑑π‘₯/𝑑𝑦+P1π‘₯=𝑄1 is (A) 𝑦 𝑒^∫1β–’γ€–P1 𝑑𝑦〗=∫1β–’γ€–(𝑄1𝑒^∫1β–’γ€–P1 𝑑𝑦〗 )𝑑𝑦+𝐢〗 (B) 𝑦. 𝑒^∫1β–’γ€–P1 𝑑π‘₯γ€—=∫1β–’γ€–(𝑄1𝑒^∫1β–’γ€–P1 𝑑π‘₯γ€— )𝑑π‘₯+𝐢〗 (C) π‘₯ 𝑒^∫1β–’γ€–P1 𝑑𝑦〗=∫1β–’γ€–(𝑄1𝑒^∫1β–’γ€–P1 𝑑𝑦〗 )𝑑𝑦+𝐢〗 (D) π‘₯ 𝑒^∫1β–’γ€–P1 𝑑π‘₯γ€—=∫1β–’γ€–(𝑄1𝑒^∫1β–’γ€–P1 𝑑π‘₯γ€— )𝑑π‘₯+𝐢〗 Differential equation is of type 𝑑π‘₯/𝑑𝑦+P1π‘₯=𝑄1 where P1 & Q1 are functions of y IF = 𝑒^∫1β–’γ€–P1 𝑑𝑦〗 General solution is x (IF) = ∫1β–’γ€–(𝑄_1×𝐼𝐹) 𝑑𝑦+𝑐〗 π‘₯ 𝑒^∫1β–’γ€–P1 𝑑𝑦〗=∫1β–’γ€–(𝑄1𝑒^∫1β–’γ€–P1 𝑑𝑦〗 ) 𝑑𝑦+𝐢〗 ∴ Option (C) is the correct answer.

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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 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.