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Example 9 - Find general solution of dy/dx = x+1 / 2-y - Variable separation - Equation given

Example 9 - Chapter 9 Class 12 Differential Equations - Part 2


Transcript

Example 9 Find the general solution of the differential equation 𝑑𝑦/𝑑π‘₯=(π‘₯+1)/(2βˆ’π‘¦) , (𝑦≠2) 𝑑𝑦/𝑑π‘₯=(π‘₯ + 1)/(2 βˆ’ 𝑦) , (𝑦≠2) (2 βˆ’ y) dy = (x + 1) dx Integrating both sides. ∫1β–’γ€–(2βˆ’π‘¦)𝑑𝑦=γ€— ∫1β–’(π‘₯+1)𝑑π‘₯ 2y βˆ’ 𝑦^2/2 = π‘₯^2/2 + x + c γ€–4𝑦 βˆ’ 𝑦〗^2/2 = (π‘₯^2+ 2π‘₯ + 2𝑐)/2 4y βˆ’ y2 = x2 + 2x + 2c 4y βˆ’ y2 = x2 + 2x + r x2 + y2 + 2x βˆ’ 4y + r = 0 is general solution

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Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.