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Ex 9.5, 2 For each of the differential equation , find the𝑑𝑦/𝑑π‘₯+3𝑦=𝑒^(βˆ’2π‘₯) Step 1: Put in form 𝑑𝑦/𝑑π‘₯ + Py = Q π’…π’š/𝒅𝒙 + 3y = 𝒆^(βˆ’πŸπ’™) Step 2: Find P and Q by comparing, we get 𝑷=πŸ‘ and Q = 𝒆^(βˆ’πŸπ’™) Step 3 : Find Integrating factor, I.F. I.F. = 𝑒^∫1▒𝑝𝑑π‘₯ I.F. = 𝑒^∫1β–’3𝑑π‘₯ general solution : 𝑑𝑦/𝑑π‘₯+3𝑦=𝑒^(βˆ’2π‘₯) I.F. = 𝒆^πŸ‘π’™ Step 4 : Solution of the equation y Γ— I.F. = ∫1▒〖𝑄×𝐼.𝐹. 𝑑π‘₯+𝑐〗 Putting values y Γ— e3x = ∫1▒𝒆^(βˆ’πŸπ’™ + πŸ‘π’™) ,dx + 𝒄 ye3x = ∫1▒𝑒^(π‘₯ ) dx + 𝑐 ye3x = 𝑒^(π‘₯ ) dx + 𝑐 Dividing by 𝑒^(3π‘₯ ) y = e–2x + Ce–3x

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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 14 years. He provides courses for Maths, Science and Computer Science at Teachoo