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Example 2 - Chapter 9 Class 12 Differential Equations
Last updated at Dec. 11, 2019 by Teachoo
Transcript
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 (๐^2 ๐ฆ)/(๐๐ฅ^2 )+๐๐ฆ/๐๐ฅโ6๐ฆ=0 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) =0 = R.H.S โด Hence Verified
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Chapter 9 Class 12 Differential Equations
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About the Author
Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.