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Ex 9.4, 6 - Find general solution: dy/dx = (1 + x2) (1 + y2) - Variable separation - Equation given


Transcript

Ex 9.4, 6 For each of the differential equations in Exercises 1 to 10, find the general solution : 𝑑𝑦/𝑑π‘₯=(1+π‘₯^2 )(1+𝑦^2 ) 𝑑𝑦/𝑑π‘₯=(1+π‘₯^2 )(1+𝑦^2 ) dy = (1+π‘₯^2 )(1+𝑦^2 ) dx 𝑑𝑦/(1 + 𝑦^2 )= (1 + π‘₯^2) dx Integrating both sides. ∫1▒𝑑𝑦/(1 + 𝑦^2 ) = ∫1β–’(1+π‘₯2)𝑑π‘₯ tanβˆ’1 y = x + 𝒙^πŸ‘/πŸ‘ + 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.