Ex 9.3, 16 - Chapter 9 Class 12 Differential Equations
Last updated at Dec. 16, 2024 by Teachoo
Ex 9.3
Ex 9.3, 1
Important
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Transcript
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)
