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
Examples
Example 1
Important
Example 2 You are here
Example 3
Example 4
Example 5
Example 6 Important
Example 7
Example 8
Example 9
Example 10
Example 11
Example 12
Example 13
Example 14 Important
Example 15 Important
Example 16
Example 17 Important
Example 18
Example 19
Example 20
Example 21
Example 22 Important
Example 23 Important
Example 24
Example 25
Example 26
Example 27 Important
Example 28 Important
Chapter 9 Class 12 Differential Equations
Serial order wise
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.