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Ex 9.3, 16 For the differential equation 𝑥𝑦 𝑑𝑦/𝑑𝑥=(𝑥+2)(𝑦+2) , find the solution curve passing through the point (1 , −1) 𝑥𝑦 𝑑𝑦/𝑑𝑥=(𝑥+2)(𝑦+2) (𝑦 𝑑𝑦)/(𝑦 + 2) = (𝑥 + 2)/𝑥 dx Integrating both sides ∫1▒𝒚/(𝒚 + 𝟐) dy = ∫1▒(𝒙 + 𝟐)/𝒙 dx ∫1▒(𝑦 + 2 − 2)/(𝑦 + 2) dy = ∫1▒(1+( 2)/𝑥) 𝑑𝑥 ∫1▒(1−( 2)/(𝑦 + 2)) dy = ∫1▒(1+( 2)/𝑥) 𝑑𝑥 y − 2 log (y + 2) = x + 2 log x + C Since curve passes through (1, − 1) Putting x = 1 and y = −1 in (1) −1 − 2 log (−1 + 2) = 1 + 2 log 1 + C −1 − 2log1 = 1 + 2log1 + C −1 = 1 + C C = −2 Put C = −2 In (1) y = 2 log (y + 2) + x + 2 log x − 2 y − x + 2 = log (y + 2)2 + log x2 y − x + 2 = log (x2 (y + 2)2)

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo