Misc 14 (MCQ) - General solution of type dx/dy + p1x = q1 is - Miscellaneous

part 2 - Misc 14 (MCQ) - Miscellaneous - Serial order wise - Chapter 9 Class 12 Differential Equations

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Misc 14 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€–ππŸ π’…π’šγ€— General solution is x (IF) = ∫1β–’γ€–(𝑄_1×𝐼𝐹) 𝑑𝑦+𝑐〗 𝒙 𝒆^∫1β–’γ€–ππŸ π’…π’šγ€—=∫1β–’γ€–(π‘ΈπŸπ’†^∫1β–’γ€–ππŸ π’…π’šγ€— ) π’…π’š+π‘ͺγ€— So, the correct answer is (c)

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