CBSE Class 12 Sample Paper for 2021 Boards

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Question 9 (Choice 2) - CBSE Class 12 Sample Paper for 2021 Boards - Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

Last updated at April 16, 2024 by

For what value of n is the following a homogeneous differential equation: dy/dx = x 3 - yn / x 2 y + xy 2

For what value of n is following a homogeneous differential equation

Question 9 (Choice 2) - CBSE Class 12 Sample Paper for 2021 Boards - Part 2

 

Transcript

Question 9 (Choice 2) For what value of n is the following a homogeneous differential equation: 𝑑𝑦/𝑑𝑥 = (𝑥^3 − 𝑦^𝑛)/(𝑥^2 𝑦 + 𝑥𝑦^2 ) Given 𝑑𝑦/𝑑𝑥 = (𝑥^3 − 𝑦^𝑛)/(𝑥^2 𝑦 + 𝑥𝑦^2 ) Thus, F(x, y) = (𝑥^3 − 𝑦^𝑛)/(𝑥^2 𝑦 + 𝑥𝑦^2 ) Since given equation is homegenous F(𝜆x, 𝜆y) = 𝜆^0 F(x, y) (〖(𝜆𝑥)〗^3 −〖 (𝜆𝑦)〗^𝑛)/((𝜆𝑥)^2 (𝜆𝑦) +(𝜆𝑥)〖(𝜆𝑦)〗^2 )=(𝑥^3 − 𝑦^𝑛)/(𝑥^2 𝑦 + 𝑥𝑦^2 ) (𝜆^3 𝑥^3 − 〖(𝜆𝑦)〗^𝑛)/(𝜆^3 𝑥^2 𝑦 +𝜆^3 𝑥𝑦^2 )=(𝑥^3 − 𝑦^𝑛)/(𝑥^2 𝑦 + 𝑥𝑦^2 ) (𝝀^𝟑 𝒙^𝟑 − 〖(𝝀𝒚)〗^𝒏)/(𝝀^𝟑 (𝒙^𝟐 𝒚 + 𝒙𝒚^𝟐))=(𝒙^𝟑 − 𝒚^𝒏)/(𝒙^𝟐 𝒚 + 𝒙𝒚^𝟐 ) This is only possible when n = 3

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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, Social Science, Physics, Chemistry, Computer Science at Teachoo.