Question 22 - CBSE Class 12 Sample Paper for 2020 Boards - Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

Last updated at Dec. 16, 2024 by Teachoo

If y = ae ^2x + be ^−x , then show that (d ² y)/(dx ² ) − dy/dx − 2y = 0

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

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

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Transcript

Question 22 If y = ae2x + be−x , then show that (𝑑^2 𝑦)/(𝑑𝑥^2 ) − 𝑑𝑦/𝑑𝑥 − 2y = 0 Given 𝑦=𝑎𝑒^2𝑥+𝑏𝑒^(−𝑥) Now, 𝑑𝑦/𝑑𝑥=2𝑎𝑒^2𝑥−𝑏𝑒^(−𝑥) And (𝑑^2 𝑦)/(𝑑𝑥^2 )=4𝑎𝑒^2𝑥+𝑏𝑒^(−𝑥) Now, We need to show (𝑑^2 𝑦)/(𝑑𝑥^2 ) − 𝑑𝑦/𝑑𝑥 − 2y = 0 Solving LHS (𝑑^2 𝑦)/(𝑑𝑥^2 ) − 𝑑𝑦/𝑑𝑥 − 2y = (4𝑎𝑒^2𝑥+𝑏𝑒^(−𝑥)) – (2𝑎𝑒^2𝑥−𝑏𝑒^(−𝑥)) – 2(𝑎𝑒^2𝑥+𝑏𝑒^(−𝑥)) = 4𝑎𝑒^2𝑥+𝑏𝑒^(−𝑥) – 2𝑎𝑒^2𝑥+𝑏𝑒^(−𝑥) – 2𝑎𝑒^2𝑥−2𝑏𝑒^(−𝑥) = (4𝑎𝑒^2𝑥 "– " 2𝑎𝑒^2𝑥 "– " 2𝑎𝑒^2𝑥)+(𝑏𝑒^(−𝑥) + 𝑏𝑒^(−𝑥) −2𝑏𝑒^(−𝑥)) = 0 + 0 = 0 Hence proved

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Davneet Singh

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

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