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Class 12
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If y = ae 2x + be βˆ’x , then show that (d 2 y)/(dx 2 ) βˆ’ dy/dx βˆ’ 2y = 0

If y = ae^2x + be^βˆ’x , then show that y'' - y' - 2y = 0 - Teachoo

Question 22 - CBSE Class 12 Sample Paper for 2020 Boards - Part 2


Transcript

Question 22 If y = ae2x + beβˆ’x , then show that (𝑑^2 𝑦)/(𝑑π‘₯^2 ) βˆ’ 𝑑𝑦/𝑑π‘₯ βˆ’ 2y = 0 Given 𝑦=π‘Žπ‘’^2π‘₯+𝑏𝑒^(βˆ’π‘₯) Now, 𝑑𝑦/𝑑π‘₯=2π‘Žπ‘’^2π‘₯βˆ’π‘π‘’^(βˆ’π‘₯) And (𝑑^2 𝑦)/(𝑑π‘₯^2 )=4π‘Žπ‘’^2π‘₯+𝑏𝑒^(βˆ’π‘₯) Now, We need to show (𝑑^2 𝑦)/(𝑑π‘₯^2 ) βˆ’ 𝑑𝑦/𝑑π‘₯ βˆ’ 2y = 0 Solving LHS (𝑑^2 𝑦)/(𝑑π‘₯^2 ) βˆ’ 𝑑𝑦/𝑑π‘₯ βˆ’ 2y = (4π‘Žπ‘’^2π‘₯+𝑏𝑒^(βˆ’π‘₯)) – (2π‘Žπ‘’^2π‘₯βˆ’π‘π‘’^(βˆ’π‘₯)) – 2(π‘Žπ‘’^2π‘₯+𝑏𝑒^(βˆ’π‘₯)) = 4π‘Žπ‘’^2π‘₯+𝑏𝑒^(βˆ’π‘₯) – 2π‘Žπ‘’^2π‘₯+𝑏𝑒^(βˆ’π‘₯) – 2π‘Žπ‘’^2π‘₯βˆ’2𝑏𝑒^(βˆ’π‘₯) = (4π‘Žπ‘’^2π‘₯ "– " 2π‘Žπ‘’^2π‘₯ "– " 2π‘Žπ‘’^2π‘₯)+(𝑏𝑒^(βˆ’π‘₯) + 𝑏𝑒^(βˆ’π‘₯) βˆ’2𝑏𝑒^(βˆ’π‘₯)) = 0 + 0 = 0 Hence proved

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Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.