# Example 2 - Chapter 9 Class 12 Differential Equations (Term 2)

Last updated at Dec. 11, 2019 by Teachoo

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 (i)

Example 1 (ii) Important

Example 1 (iii) Important

Example 2 You are here

Example 3 Important

Example 4 Deleted for CBSE Board 2022 Exams

Example 5 Deleted for CBSE Board 2022 Exams

Example 6 Important Deleted for CBSE Board 2022 Exams

Example 7 Deleted for CBSE Board 2022 Exams

Example 8 Deleted for CBSE Board 2022 Exams

Example 9

Example 10

Example 11

Example 12 Important

Example 13

Example 14 Important

Example 15 Important

Example 16

Example 17 Important

Example 18 Important

Example 19

Example 20 Important

Example 21 Deleted for CBSE Board 2022 Exams

Example 22 Important

Example 23 Important

Example 24

Example 25 Deleted for CBSE Board 2022 Exams

Example 26

Example 27 Important

Example 28 Important Deleted for CBSE Board 2022 Exams

Chapter 9 Class 12 Differential Equations (Term 2)

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Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.