Write the general solution of differential equation dy/dx = e (x+y)

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Transcript

Question 20 Write the general solution of differential equation ๐‘‘๐‘ฆ/๐‘‘๐‘ฅ = ๐‘’^(๐‘ฅ+๐‘ฆ) Given ๐‘‘๐‘ฆ/๐‘‘๐‘ฅ = ๐‘’^(๐‘ฅ+๐‘ฆ) ๐‘‘๐‘ฆ/๐‘‘๐‘ฅ = ๐‘’^๐‘ฅ.๐‘’^๐‘ฆ ๐‘‘๐‘ฆ/๐‘’^๐‘ฆ = ๐‘’^๐‘ฅ ๐‘‘๐‘ฅ e^(โˆ’๐‘ฆ) ๐‘‘๐‘ฆ = ๐‘’^๐‘ฅ ๐‘‘๐‘ฅ Integrating both sides โˆซ1โ–’ใ€–e^(โˆ’๐‘ฆ) ๐‘‘๐‘ฆใ€— = โˆซ1โ–’ใ€–๐‘’^๐‘ฅ ๐‘‘๐‘ฅ" " ใ€— โˆ’๐‘’^(โˆ’๐‘ฆ) = ๐‘’^๐‘ฅ+๐‘ 0 = ๐‘’^๐‘ฅ+๐‘’^(โˆ’๐‘ฆ)+ C Or we can write it as ๐’†^๐’™+๐’†^(โˆ’๐’š)= C Thus, the general solution is ๐’†^๐’™+๐’†^(โˆ’๐’š)= C

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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.