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

Examples 9 last slide.jpg

  1. Chapter 9 Class 12 Differential Equations
  2. Serial order wise

Transcript

Example 9 Find the general solution of the differential equation ๐‘‘๐‘ฆ/๐‘‘๐‘ฅ=(๐‘ฅ+1)/(2โˆ’๐‘ฆ) , (๐‘ฆโ‰ 2) ๐‘‘๐‘ฆ/๐‘‘๐‘ฅ=(๐‘ฅ + 1)/(2 โˆ’ ๐‘ฆ) , (๐‘ฆโ‰ 2) (2 โˆ’ y) dy = (x + 1) dx Integrating both sides. โˆซ1โ–’ใ€–(2โˆ’๐‘ฆ)๐‘‘๐‘ฆ=ใ€— โˆซ1โ–’(๐‘ฅ+1)๐‘‘๐‘ฅ 2y โˆ’ ๐‘ฆ^2/2 = ๐‘ฅ^2/2 + x + c ใ€–4๐‘ฆ โˆ’ ๐‘ฆใ€—^2/2 = (๐‘ฅ^2+ 2๐‘ฅ + 2๐‘)/2 4y โˆ’ y2 = x2 + 2x + 2c 4y โˆ’ y2 = x2 + 2x + r x2 + y2 + 2x โˆ’ 4y + r = 0 is general solution

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.