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Ex 9.4, 16 - For xy dy/dx = (x + 2) (y + 2), find solution - Variable separation - Equation given

Ex 9.4, 16 - Chapter 9 Class 12 Differential Equations - Part 2


Transcript

Ex 9.4, 16 For the differential equation / =( +2)( +2) , find the solution curve passing through the point (1 , 1) / =( +2)( +2) ( )/( + 2) = ( + 2)/ dx Integrating both sides 1 /( + 2) dy = 1 ( + 2)/ dx 1 ( + 2 2)/( + 2) dy = 1 (1+( 2)/ ) 1 (1 ( 2)/( + 2)) dy = 1 (1+( 2)/ ) 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 has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.