Find the general solution of the following differential equation: ๐ฅ ๐๐ฆ − (๐ฆ + 2๐ฅ ^{ 2 } )๐๐ฅ = 0
CBSE Class 12 Sample Paper for 2021 Boards
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CBSE Class 12 Sample Paper for 2021 Boards
Last updated at April 16, 2024 by Teachoo
Question 35 Find the general solution of the following differential equation: ๐ฅ ๐๐ฆ โ (๐ฆ + 2๐ฅ2 )๐๐ฅ = 0 Given ๐ฅ ๐๐ฆ = (๐ฆ + 2๐ฅ2 )๐๐ฅ ๐๐ฆ/๐๐ฅ=(๐ฆ + 2๐ฅ^2)/๐ฅ ๐๐ฆ/๐๐ฅ=๐ฆ/๐ฅ+2๐ฅ ๐ ๐/๐ ๐โ๐/๐=๐๐ Comparing with ๐ ๐/๐ ๐ + Py = Q โด P = (โ1)/๐ฅ and Q = 2x Find integrating factor IF IF = e^โซ1โ๐๐๐ฅ IF = ๐^โซ1โใ(โ1)/๐ฅ ๐๐ฅใ IF = ๐^(โlogโก๐ฅ ) IF = ๐^logโกใ(๐ฅ)^(โ1) ใ IF = ๐^ใlog ใโกใ1/๐ฅใ IF = ๐/๐ Solution of the equation y ร I.F = โซ1โใ๐ธ ร ๐ฐ.๐ญ.๐ ๐+๐ ใ Putting values, ๐ฆ ร1/๐ฅ = โซ1โใ2๐ฅ ร1/๐ฅ ๐๐ฅใ+๐ถ ๐ฆ/๐ฅ = โซ1โ2๐๐ฅ+๐ถ ๐ฆ/๐ฅ = 2๐ฅ+๐ถ ๐ = ๐๐^๐+๐ช๐