Ex 9.3, 12 - Which equations has y = x as particular solution - Ex 9.3

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  1. Chapter 9 Class 12 Differential Equations
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Ex 9.3, 12 Which of the following differential equations has ๐‘ฆ=๐‘ฅ as one of its particular solution ? (A) (๐‘‘^2 ๐‘ฆ)/(๐‘‘๐‘ฅ^2 )โˆ’๐‘ฅ^2 ๐‘‘๐‘ฆ/๐‘‘๐‘ฅ+๐‘ฅ๐‘ฆ=๐‘ฅ (B) (๐‘‘^2 ๐‘ฆ)/(๐‘‘๐‘ฅ^2 )+๐‘ฅ ๐‘‘๐‘ฆ/๐‘‘๐‘ฅ+๐‘ฅ๐‘ฆ=๐‘ฅ (C) ) (๐‘‘^2 ๐‘ฆ)/(๐‘‘๐‘ฅ^2 )โˆ’๐‘ฅ^2 ๐‘‘๐‘ฆ/๐‘‘๐‘ฅ+๐‘ฅ๐‘ฆ=0 (D) (๐‘‘^2 ๐‘ฆ)/(๐‘‘๐‘ฅ^2 )+๐‘ฅ ๐‘‘๐‘ฆ/๐‘‘๐‘ฅ+๐‘ฅ๐‘ฆ=0 ๐‘ฆ=๐‘ฅ Differentiating both sides w.r.t. ๐‘ฅ ๐‘‘๐‘ฆ/๐‘‘๐‘ฅ=1 Again differentiating both sides w.r.t. ๐‘ฅ โˆด (๐‘‘^2 ๐‘ฆ)/(๐‘‘๐‘ฅ^2 )=0 Let us check each Options Option A (๐‘‘^2 ๐‘ฆ)/(๐‘‘๐‘ฅ^2 ) โˆ’๐‘ฅ^2 ๐‘‘๐‘ฆ/๐‘‘๐‘ฅ +๐‘ฅ๐‘ฆ=๐‘ฅ 0โˆ’๐‘ฅ^2 (1)+๐‘ฅ๐‘ฆ=๐‘ฅ โˆ’๐‘ฅ^2+๐‘ฅ๐‘ฆ=๐‘ฅ โˆ’๐‘ฅ^2+๐‘ฅ(๐‘ฅ)=๐‘ฅ โˆ’๐‘ฅ^2+๐‘ฅ^2=๐‘ฅ 0=๐‘ฅ โˆด Option (A) is not possible Option B (๐‘‘^2 ๐‘ฆ)/(๐‘‘๐‘ฅ^2 ) +๐‘ฅ ๐‘‘๐‘ฆ/๐‘‘๐‘ฅ+๐‘ฅ๐‘ฆ=๐‘ฅ 0โˆ’๐‘ฅ(1)+๐‘ฅ๐‘ฆ=๐‘ฅ ๐‘ฅ+๐‘ฅ๐‘ฆ=๐‘ฅ ๐‘ฅ๐‘ฆ=๐‘ฅโˆ’๐‘ฅ ๐‘ฅ๐‘ฆ=๐‘ฅโˆ’๐‘ฅ ๐‘ฅ(๐‘ฅ)=0 ๐‘ฅ^2=0 โˆด Option (B) is not possible Option C (๐‘‘^2 ๐‘ฆ)/(๐‘‘๐‘ฅ^2 )โˆ’๐‘ฅ^2 ๐‘‘๐‘ฆ/๐‘‘๐‘ฅ+๐‘ฅ๐‘ฆ=0 0โˆ’๐‘ฅ^2 (1)+๐‘ฅ๐‘ฆ=0 โˆ’๐‘ฅ^2+๐‘ฅ๐‘ฆ=0 โˆ’๐‘ฅ^2+๐‘ฅ(๐‘ฅ)=0 โˆ’๐‘ฅ^2+๐‘ฅ^2=0 0=0 โˆด Option (C) is possible Option D (๐‘‘^2 ๐‘ฆ)/(๐‘‘๐‘ฅ^2 ) +๐‘ฅ ๐‘‘๐‘ฆ/๐‘‘๐‘ฅ+๐‘ฅ๐‘ฆ=0 0โˆ’๐‘ฅ(1)+๐‘ฅ๐‘ฆ=0 ๐‘ฅ+๐‘ฅ๐‘ฆ=0 ๐‘ฅ+๐‘ฅ(๐‘ฅ)=0 ๐‘ฅ+๐‘ฅ^2=0 ๐‘ฅ^2=โˆ’๐‘ฅ โˆด Option (C) is not possible โˆด Option c is correct

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Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.