1. Chapter 9 Class 12 Differential Equations
  2. Serial order wise
  3. Ex 9.3
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Ex 9.3, 16 - Chapter 9 Class 12 Differential Equations

Last updated at Dec. 16, 2024 by Teachoo

Transcript

Ex 9.3, 16 For the differential equation ๐‘ฅ๐‘ฆ ๐‘‘๐‘ฆ/๐‘‘๐‘ฅ=(๐‘ฅ+2)(๐‘ฆ+2) , find the solution curve passing through the point (1 , โˆ’1) ๐‘ฅ๐‘ฆ ๐‘‘๐‘ฆ/๐‘‘๐‘ฅ=(๐‘ฅ+2)(๐‘ฆ+2) (๐‘ฆ ๐‘‘๐‘ฆ)/(๐‘ฆ + 2) = (๐‘ฅ + 2)/๐‘ฅ dx Integrating both sides โˆซ1โ–’๐’š/(๐’š + ๐Ÿ) dy = โˆซ1โ–’(๐’™ + ๐Ÿ)/๐’™ dx โˆซ1โ–’(๐‘ฆ + 2 โˆ’ 2)/(๐‘ฆ + 2) dy = โˆซ1โ–’(1+( 2)/๐‘ฅ) ๐‘‘๐‘ฅ โˆซ1โ–’(1โˆ’( 2)/(๐‘ฆ + 2)) dy = โˆซ1โ–’(1+( 2)/๐‘ฅ) ๐‘‘๐‘ฅ y โˆ’ 2 log (y + 2) = x + 2 log x + C Since curve passes through (1, โˆ’ 1) Putting x = 1 and y = โˆ’1 in (1) โˆ’1 โˆ’ 2 log (โˆ’1 + 2) = 1 + 2 log 1 + C โˆ’1 โˆ’ 2log1 = 1 + 2log1 + C โˆ’1 = 1 + C C = โˆ’2 Put C = โˆ’2 In (1) y = 2 log (y + 2) + x + 2 log x โˆ’ 2 y โˆ’ x + 2 = log (y + 2)2 + log x2 y โˆ’ x + 2 = log (x2 (y + 2)2)
  1. Chapter 9 Class 12 Differential Equations
  2. Serial order wise

    3. Ex 9.3

    Ex 9.4 →
Ex 9.4 →
Chapter 9 Class 12 Differential Equations
Serial order wise

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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