Ex 9.5, 2 - Chapter 9 Class 12 Differential Equations
Last updated at April 16, 2024 by Teachoo
Solving Linear differential equations - Equation given
Ex 9.5, 19 (MCQ) Important
Misc 14 (MCQ) Important
Ex 9.5, 2 You are here
Ex 9.5, 10
Ex 9.5, 3 Important
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Misc 15 (MCQ)
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Ex 9.5, 8 Important
Misc 10 Important
Misc 11
Ex 9.5, 14 Important
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Example 14
Ex 9.5, 1 Important
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Ex 9.5, 11
Example 16
Example 17 Important
Example 22 Important
Solving Linear differential equations - Equation given
Last updated at April 16, 2024 by Teachoo
Ex 9.5, 2 For each of the differential equation , find theππ¦/ππ₯+3π¦=π^(β2π₯) Step 1: Put in form ππ¦/ππ₯ + Py = Q π π/π π + 3y = π^(βππ) Step 2: Find P and Q by comparing, we get π·=π and Q = π^(βππ) Step 3 : Find Integrating factor, I.F. I.F. = π^β«1βπππ₯ I.F. = π^β«1β3ππ₯ general solution : ππ¦/ππ₯+3π¦=π^(β2π₯) I.F. = π^ππ Step 4 : Solution of the equation y Γ I.F. = β«1βγπΓπΌ.πΉ. ππ₯+πγ Putting values y Γ e3x = β«1βπ^(βππ + ππ) ,dx + π ye3x = β«1βπ^(π₯ ) dx + π ye3x = π^(π₯ ) dx + π Dividing by π^(3π₯ ) y = eβ2x + Ceβ3x