Example 2 - Chapter 9 Class 12 Differential Equations
Last updated at Dec. 16, 2024 by Teachoo
Last updated at Dec. 16, 2024 by Teachoo
Example 2 Verify that the function ๐ฆ=๐^(โ3๐ฅ) is a solution of the differential equation (๐^2 ๐ฆ)/(๐๐ฅ^2 )+๐๐ฆ/๐๐ฅโ6๐ฆ=0 ๐ฆ=๐^(โ3๐ฅ) ๐ ๐/๐ ๐=๐(๐^(โ3๐ฅ) )/๐๐ฅ ๐๐ฆ/๐๐ฅ=ใโ3 ๐ใ^(โ3๐ฅ) (๐ ^๐ ๐)/(๐ ๐^๐ )=๐/๐๐ฅ (๐๐ฆ/๐๐ฅ) =๐(ใโ3 ๐ใ^(โ3๐ฅ) )/๐๐ฅ =โ3 ๐(๐^(โ3๐ฅ) )/๐๐ฅ =โ3 ร (ใโ3 ๐ใ^(โ3๐ฅ) ) = ใ9 ๐ใ^(โ3๐ฅ) Now, we have to verify (๐ ^๐ ๐)/(๐ ๐^๐ )+๐ ๐/๐ ๐โ๐๐=๐ Solving L.H.S (๐^2 ๐ฆ)/(๐๐ฅ^2 )+๐๐ฆ/๐๐ฅโ6๐ฆ Putting values = ใ9 ๐ใ^(โ3๐ฅ)+(โ3๐^(โ3๐ฅ) )โ6(๐^(โ3๐ฅ) ) =ใ9 ๐ใ^(โ3๐ฅ)โ3๐^(โ3๐ฅ)โ6๐^(โ3๐ฅ) =ใ9 ๐ใ^(โ3๐ฅ)โ9๐^(โ3๐ฅ) =๐ = R.H.S โด Hence Verified
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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