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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


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 is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.