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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

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.