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  1. Chapter 9 Class 12 Differential Equations
  2. Serial order wise

Transcript

Ex 9.3, 11 Which of the following differential equations has ๐‘ฆ=๐‘1๐‘’^๐‘ฅ+๐‘2๐‘’^(โˆ’๐‘ฅ) as the general solution ? (A) (๐‘‘^2 ๐‘ฆ)/(๐‘‘๐‘ฅ^2 )+๐‘ฆ=0 (B) (๐‘‘^2 ๐‘ฆ)/(๐‘‘๐‘ฅ^2 )โˆ’๐‘ฆ=0 (C) (๐‘‘^2 ๐‘ฆ)/(๐‘‘๐‘ฅ^2 )+1=0 (D) (๐‘‘^2 ๐‘ฆ)/(๐‘‘๐‘ฅ^2 )โˆ’๐‘ฆ=0 ๐‘ฆ=๐‘1๐‘’^๐‘ฅ+๐‘2๐‘’^(โˆ’๐‘ฅ) โˆด Differentiating both sides w.r.t. ๐‘ฅ ๐‘‘๐‘ฆ/๐‘‘๐‘ฅ =๐‘1๐‘’^๐‘ฅโˆ’๐‘2๐‘’^(โˆ’๐‘ฅ) Again Differentiating both sides w.r.t. x (๐‘‘^2 ๐‘ฆ)/(๐‘‘๐‘ฅ^2 ) =๐‘1๐‘’^๐‘ฅโˆ’๐‘2๐‘’^(โˆ’๐‘ฅ) (โˆ’1) Since it has two variables, we will differentiate twice (๐‘‘^2 ๐‘ฆ)/(๐‘‘๐‘ฅ^2 ) =๐‘1๐‘’^๐‘ฅ+๐‘2๐‘’^(โˆ’๐‘ฅ) (๐‘‘^2 ๐‘ฆ)/(๐‘‘๐‘ฅ^2 )=๐‘ฆ (๐‘‘^2 ๐‘ฆ)/(๐‘‘๐‘ฅ^2 ) โˆ’๐‘ฆ=0 โˆด Option B is correct (Putting ๐‘ฆ=๐‘1๐‘’^๐‘ฅ+๐‘2๐‘’^(โˆ’๐‘ฅ))

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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.