



Ex 9.3
Ex 9.3, 2 Deleted for CBSE Board 2022 Exams
Ex 9.3, 3 Important Deleted for CBSE Board 2022 Exams
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Ex 9.3, 5 Important Deleted for CBSE Board 2022 Exams
Ex 9.3, 6 Deleted for CBSE Board 2022 Exams
Ex 9.3, 7 Important Deleted for CBSE Board 2022 Exams
Ex 9.3, 8 Deleted for CBSE Board 2022 Exams
Ex 9.3, 9 Deleted for CBSE Board 2022 Exams
Ex 9.3, 10 Important Deleted for CBSE Board 2022 Exams
Ex 9.3, 11 (MCQ) Deleted for CBSE Board 2022 Exams
Ex 9.3, 12 (MCQ) Important Deleted for CBSE Board 2022 Exams You are here
Last updated at Aug. 20, 2021 by Teachoo
Ex 9.3, 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