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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 August 10, 2026 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

 

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Question 9 (Choice 2) For what value of n is the following a homogeneous differential equation: š‘‘š‘¦/š‘‘š‘„ = (š‘„^3 āˆ’ š‘¦^š‘›)/(š‘„^2 š‘¦ + š‘„š‘¦^2 ) Given š‘‘š‘¦/š‘‘š‘„ = (š‘„^3 āˆ’ š‘¦^š‘›)/(š‘„^2 š‘¦ + š‘„š‘¦^2 ) Thus, F(x, y) = (š‘„^3 āˆ’ š‘¦^š‘›)/(š‘„^2 š‘¦ + š‘„š‘¦^2 ) Since given equation is homegenous F(šœ†x, šœ†y) = šœ†^0 F(x, y) (怖(šœ†š‘„)怗^3 āˆ’怖 (šœ†š‘¦)怗^š‘›)/((šœ†š‘„)^2 (šœ†š‘¦) +(šœ†š‘„)怖(šœ†š‘¦)怗^2 )=(š‘„^3 āˆ’ š‘¦^š‘›)/(š‘„^2 š‘¦ + š‘„š‘¦^2 ) (šœ†^3 š‘„^3 āˆ’ 怖(šœ†š‘¦)怗^š‘›)/(šœ†^3 š‘„^2 š‘¦ +šœ†^3 š‘„š‘¦^2 )=(š‘„^3 āˆ’ š‘¦^š‘›)/(š‘„^2 š‘¦ + š‘„š‘¦^2 ) (š€^šŸ‘ š’™^šŸ‘ āˆ’ 怖(š€š’š)怗^š’)/(š€^šŸ‘ (š’™^šŸ š’š + š’™š’š^šŸ))=(š’™^šŸ‘ āˆ’ š’š^š’)/(š’™^šŸ š’š + š’™š’š^šŸ ) This is only possible when n = 3

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