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

Ex 9.3, 12 - Chapter 9 Class 12 Differential Equations - Part 2
Ex 9.3, 12 - Chapter 9 Class 12 Differential Equations - Part 3
Ex 9.3, 12 - Chapter 9 Class 12 Differential Equations - Part 4
Ex 9.3, 12 - Chapter 9 Class 12 Differential Equations - Part 5

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Question 12 Which of the following differential equations has 𝑦=𝑥 as one of its particular solution ? (A) (𝑑^2 𝑦)/(𝑑𝑥^2 )−𝑥^2 𝑑𝑦/𝑑𝑥+𝑥𝑦=𝑥 (B) (𝑑^2 𝑦)/(𝑑𝑥^2 )+𝑥 𝑑𝑦/𝑑𝑥+𝑥𝑦=𝑥 (C) ) (𝑑^2 𝑦)/(𝑑𝑥^2 )−𝑥^2 𝑑𝑦/𝑑𝑥+𝑥𝑦=0 (D) (𝑑^2 𝑦)/(𝑑𝑥^2 )+𝑥 𝑑𝑦/𝑑𝑥+𝑥𝑦=0 𝑦=𝑥 Differentiating both sides w.r.t. 𝑥 𝑑𝑦/𝑑𝑥=1 Again differentiating both sides w.r.t. 𝑥 (𝑑^2 𝑦)/(𝑑𝑥^2 )=0 Let us check each Options Option A (𝑑^2 𝑦)/(𝑑𝑥^2 ) −𝑥^2 𝑑𝑦/𝑑𝑥 +𝑥𝑦=𝑥 Putting (𝑑^2 𝑦)/(𝑑𝑥^2 ) = 1, 𝑑𝑦/𝑑𝑥 = 0, y = x 0−𝑥^2 (1)+𝑥(𝑥)=𝑥 −𝑥^2+𝑥^2=𝑥 0=𝑥 Since this is not true ∴ Option (A) is not possible Option B (𝑑^2 𝑦)/(𝑑𝑥^2 ) +𝑥 𝑑𝑦/𝑑𝑥+𝑥𝑦=𝑥 Putting (𝑑^2 𝑦)/(𝑑𝑥^2 ) = 1, 𝑑𝑦/𝑑𝑥 = 0, y = x 0+𝑥(1)+𝑥(𝑥)=𝑥 𝑥+𝑥^2=𝑥 𝑥^2=0 Since this is not true ∴ Option (B) is not possible Option C (𝑑^2 𝑦)/(𝑑𝑥^2 )−𝑥^2 𝑑𝑦/𝑑𝑥+𝑥𝑦=0 Putting (𝑑^2 𝑦)/(𝑑𝑥^2 ) = 1, 𝑑𝑦/𝑑𝑥 = 0, y = x 0−𝑥^2 (1)+𝑥(𝑥)=0 −𝑥^2+𝑥^2=0 0=0 Since this is true ∴ Option (C) is possible Option D (𝑑^2 𝑦)/(𝑑𝑥^2 ) +𝑥 𝑑𝑦/𝑑𝑥+𝑥𝑦=0 Putting (𝑑^2 𝑦)/(𝑑𝑥^2 ) = 1, 𝑑𝑦/𝑑𝑥 = 0, y = x 0+𝑥(1)+𝑥(𝑥)=0 𝑥+𝑥^2=0 𝑥=−𝑥^2 Since this is not true ∴ Option (D) is not possible Thus, Option C is correct

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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