CBSE Class 12 Sample Paper for 2021 Boards

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Question 35 - CBSE Class 12 Sample Paper for 2021 Boards - Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

Last updated at December 16, 2024 by

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

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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

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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’™

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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