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

Transcript

Ex 9.4, 3 For each of the differential equations in Exercises 1 to 10, find the general solution : ๐‘‘๐‘ฆ/๐‘‘๐‘ฅ+๐‘ฆ=1(๐‘ฆโ‰ 1) ๐‘‘๐‘ฆ/๐‘‘๐‘ฅ+๐‘ฆ=1 ๐‘‘๐‘ฆ/๐‘‘๐‘ฅ=1โˆ’๐‘ฆ ๐‘‘๐‘ฆ = (1 โˆ’ y) dx ๐‘‘๐‘ฆ/(1 โˆ’ ๐‘ฆ) = dx ๐‘‘๐‘ฆ/(๐‘ฆ โˆ’ 1) = โˆ’dx Integrating both sides. โˆซ1โ–’ใ€–๐‘‘๐‘ฆ/(๐‘ฆ โˆ’ 1)=ใ€— โˆซ1โ–’ใ€–โˆ’๐‘‘๐‘ฅใ€— log (y โˆ’ 1) = โˆ’x + C y โˆ’ 1 = e(โˆ’x + C) y โˆ’ 1 = eโˆ’x ร— eC y = eโˆ’x ร— eC + 1 Putting eC = A y = Aeโˆ’x + 1 is the 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.