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Ex 9.3, 11 - Which differential equations has y = c1 ex + c2 e-x

Ex 9.3, 11 - Chapter 9 Class 12 Differential Equations - Part 2

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Question 11 Which of the following differential equations has 𝑦=𝑐1𝑒^π‘₯+𝑐2𝑒^(βˆ’π‘₯) as the general solution ? (A) (𝑑^2 𝑦)/(𝑑π‘₯^2 )+𝑦=0 (B) (𝑑^2 𝑦)/(𝑑π‘₯^2 )βˆ’π‘¦=0 (C) (𝑑^2 𝑦)/(𝑑π‘₯^2 )+1=0 (D) (𝑑^2 𝑦)/(𝑑π‘₯^2 )βˆ’π‘¦=0 𝑦=𝑐1𝑒^π‘₯+𝑐2𝑒^(βˆ’π‘₯) ∴ Differentiating both sides w.r.t. π‘₯ 𝑑𝑦/𝑑π‘₯ =𝑐1𝑒^π‘₯βˆ’π‘2𝑒^(βˆ’π‘₯) Again Differentiating both sides w.r.t. x (𝑑^2 𝑦)/(𝑑π‘₯^2 ) =𝑐1𝑒^π‘₯βˆ’π‘2𝑒^(βˆ’π‘₯) (βˆ’1) Since it has two variables, we will differentiate twice (𝑑^2 𝑦)/(𝑑π‘₯^2 ) =𝑐1𝑒^π‘₯+𝑐2𝑒^(βˆ’π‘₯) (𝑑^2 𝑦)/(𝑑π‘₯^2 )=𝑦 (𝑑^2 𝑦)/(𝑑π‘₯^2 ) βˆ’π‘¦=0 ∴ Option B is correct (Putting 𝑦=𝑐1𝑒^π‘₯+𝑐2𝑒^(βˆ’π‘₯))

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.