If y = ae ^{ 2x } + be ^{ −x } , then show that (d ^{ 2 } y)/(dx ^{ 2 } ) − dy/dx − 2y = 0
Last updated at Oct. 17, 2019 by Teachoo
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Question 22 If y = ae2x + beโx , then show that (๐^2 ๐ฆ)/(๐๐ฅ^2 ) โ ๐๐ฆ/๐๐ฅ โ 2y = 0 Given ๐ฆ=๐๐^2๐ฅ+๐๐^(โ๐ฅ) Now, ๐๐ฆ/๐๐ฅ=2๐๐^2๐ฅโ๐๐^(โ๐ฅ) And (๐^2 ๐ฆ)/(๐๐ฅ^2 )=4๐๐^2๐ฅ+๐๐^(โ๐ฅ) Now, We need to show (๐^2 ๐ฆ)/(๐๐ฅ^2 ) โ ๐๐ฆ/๐๐ฅ โ 2y = 0 Solving LHS (๐^2 ๐ฆ)/(๐๐ฅ^2 ) โ ๐๐ฆ/๐๐ฅ โ 2y = (4๐๐^2๐ฅ+๐๐^(โ๐ฅ)) โ (2๐๐^2๐ฅโ๐๐^(โ๐ฅ)) โ 2(๐๐^2๐ฅ+๐๐^(โ๐ฅ)) = 4๐๐^2๐ฅ+๐๐^(โ๐ฅ) โ 2๐๐^2๐ฅ+๐๐^(โ๐ฅ) โ 2๐๐^2๐ฅโ2๐๐^(โ๐ฅ) = (4๐๐^2๐ฅ "โ " 2๐๐^2๐ฅ "โ " 2๐๐^2๐ฅ)+(๐๐^(โ๐ฅ) + ๐๐^(โ๐ฅ) โ2๐๐^(โ๐ฅ)) = 0 + 0 = 0 Hence proved
CBSE Class 12 Sample Paper for 2020 Boards
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CBSE Class 12 Sample Paper for 2020 Boards
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