Find the general solution of the following differential equation: ๐‘ฅ ๐‘‘๐‘ฆ − (๐‘ฆ + 2๐‘ฅ 2 )๐‘‘๐‘ฅ = 0

 

Find general solution of differential equation: xdy - (y + 2x^2)dx = 0

Question 35 - CBSE Class 12 Sample Paper for 2021 Boards - Part 2
Question 35 - CBSE Class 12 Sample Paper for 2021 Boards - Part 3

  1. Class 12
  2. Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

Transcript

Question 35 Find the general solution of the following differential equation: ๐‘ฅ ๐‘‘๐‘ฆ โˆ’ (๐‘ฆ + 2๐‘ฅ2 )๐‘‘๐‘ฅ = 0 Given ๐‘ฅ ๐‘‘๐‘ฆ = (๐‘ฆ + 2๐‘ฅ2 )๐‘‘๐‘ฅ ๐‘‘๐‘ฆ/๐‘‘๐‘ฅ=(๐‘ฆ + 2๐‘ฅ^2)/๐‘ฅ ๐‘‘๐‘ฆ/๐‘‘๐‘ฅ=๐‘ฆ/๐‘ฅ+2๐‘ฅ ๐’…๐’š/๐’…๐’™โˆ’๐’š/๐’™=๐Ÿ๐’™ Comparing with ๐’…๐’š/๐’…๐’™ + Py = Q โˆด P = (โˆ’1)/๐‘ฅ and Q = 2x Find integrating factor IF IF = e^โˆซ1โ–’๐‘ƒ๐‘‘๐‘ฅ IF = ๐‘’^โˆซ1โ–’ใ€–(โˆ’1)/๐‘ฅ ๐‘‘๐‘ฅใ€— IF = ๐‘’^(โˆ’logโก๐‘ฅ ) IF = ๐‘’^logโกใ€–(๐‘ฅ)^(โˆ’1) ใ€— IF = ๐‘’^ใ€–log ใ€—โกใ€–1/๐‘ฅใ€— IF = ๐Ÿ/๐’™ Solution of the equation y ร— I.F = โˆซ1โ–’ใ€–๐‘ธ ร— ๐‘ฐ.๐‘ญ.๐’…๐’™+๐’„ ใ€— Putting values, ๐‘ฆ ร—1/๐‘ฅ = โˆซ1โ–’ใ€–2๐‘ฅ ร—1/๐‘ฅ ๐‘‘๐‘ฅใ€—+๐ถ ๐‘ฆ/๐‘ฅ = โˆซ1โ–’2๐‘‘๐‘ฅ+๐ถ ๐‘ฆ/๐‘ฅ = 2๐‘ฅ+๐ถ ๐’š = ๐Ÿ๐’™^๐Ÿ+๐‘ช๐’™

Class 12
Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.