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Ex 9.5, 2 - Chapter 9 Class 12 Differential Equations
Last updated at May 29, 2023 by Teachoo
Ex 9.5
Ex 9.5, 1
Important
Ex 9.5, 2 You are here
Ex 9.5, 3 Important
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Ex 9.5, 18 (MCQ)
Ex 9.5, 19 (MCQ) Important
Transcript
Ex 9.5, 2 For each of the differential equation , find the general solution : 𝑑𝑦𝑑𝑥+3𝑦= 𝑒−2𝑥 𝑑𝑦𝑑𝑥+3𝑦= 𝑒−2𝑥 Step 1: Put in form 𝑑𝑦𝑑𝑥 + Py = Q 𝑑𝑦𝑑𝑥 + 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. = 𝑒3𝑥 Step 4 : Solution of the equation y × I.F. = 𝑄×𝐼.𝐹. 𝑑𝑥+𝑐 Putting values y × e3x = 𝑒−2𝑥 + 3𝑥 ,dx + 𝑐 ye3x = 𝑒𝑥 dx + 𝑐 ye3x = 𝑒𝑥 dx + 𝑐 Dividing by 𝑒3𝑥 y = e–2x + Ce–3x
