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

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

Question 20 - CBSE Class 12 Sample Paper for 2020 Boards - Part 2


Transcript

Question 20 Write the general solution of differential equation 𝑑𝑦/𝑑π‘₯ = 𝑒^(π‘₯+𝑦) Given 𝑑𝑦/𝑑π‘₯ = 𝑒^(π‘₯+𝑦) 𝑑𝑦/𝑑π‘₯ = 𝑒^π‘₯.𝑒^𝑦 𝑑𝑦/𝑒^𝑦 = 𝑒^π‘₯ 𝑑π‘₯ e^(βˆ’π‘¦) 𝑑𝑦 = 𝑒^π‘₯ 𝑑π‘₯ Integrating both sides ∫1β–’γ€–e^(βˆ’π‘¦) 𝑑𝑦〗 = ∫1▒〖𝑒^π‘₯ 𝑑π‘₯" " γ€— βˆ’π‘’^(βˆ’π‘¦) = 𝑒^π‘₯+𝑐 0 = 𝑒^π‘₯+𝑒^(βˆ’π‘¦)+ C Or we can write it as 𝒆^𝒙+𝒆^(βˆ’π’š)= C Thus, the general solution is 𝒆^𝒙+𝒆^(βˆ’π’š)= C

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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.