Check sibling questions

Ex 9.6, 2 - Find general solution: dy/dx + 3y = e-2x - Solving Linear differential equations - Equation given

Ex 9.6, 2 - Chapter 9 Class 12 Differential Equations - Part 2


Transcript

Ex 9.6, 2 For each of the differential equation , find the general solution : 𝑑𝑦﷮𝑑𝑥﷯+3𝑦= 𝑒﷮−2𝑥﷯ 𝑑𝑦﷮𝑑𝑥﷯+3𝑦= 𝑒﷮−2𝑥﷯ Step 1: Put in form 𝑑𝑦﷮𝑑𝑥﷯ + Py = Q 𝑑𝑦﷮𝑑𝑥﷯ + 3y = 𝑒﷮−2𝑥﷯ Step 2: Find P and Q by comparing, we get 𝑃=3 and Q = 𝑒﷮−2𝑥﷯ Step 3 : Find Integrating factor, I.F. I.F. = 𝑒﷮ ﷮﷮𝑝𝑑𝑥﷯﷯ I.F. = 𝑒﷮ ﷮﷮3𝑑𝑥﷯﷯ I.F. = 𝑒﷮3𝑥﷯ Step 4 : Solution of the equation y × I.F. = ﷮﷮𝑄×𝐼.𝐹. 𝑑𝑥+𝑐﷯ Putting values y × e3x = ﷮﷮ 𝑒﷮−2𝑥 + 3𝑥﷯﷯ ,dx + 𝑐 ye3x = ﷮﷮ 𝑒﷮𝑥 ﷯﷯ dx + 𝑐 ye3x = 𝑒﷮𝑥 ﷯ dx + 𝑐 Dividing by 𝑒﷮3𝑥 ﷯ y = e–2x + Ce–3x

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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.