Question 12 (MCQ) - Forming Differential equations - Chapter 9 Class 12 Differential Equations
Last updated at April 16, 2024 by Teachoo
Forming Differential equations
Last updated at April 16, 2024 by Teachoo
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