CBSE Class 12 Sample Paper for 2021 Boards

Class 12
Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

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

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Question 9 (Choice 2) For what value of n is the following a homogeneous differential equation: ππ¦/ππ₯ = (π₯^3 β π¦^π)/(π₯^2 π¦ + π₯π¦^2 ) Given ππ¦/ππ₯ = (π₯^3 β π¦^π)/(π₯^2 π¦ + π₯π¦^2 ) Thus, F(x, y) = (π₯^3 β π¦^π)/(π₯^2 π¦ + π₯π¦^2 ) Since given equation is homegenous F(πx, πy) = π^0 F(x, y) (γ(ππ₯)γ^3 βγ (ππ¦)γ^π)/((ππ₯)^2 (ππ¦) +(ππ₯)γ(ππ¦)γ^2 )=(π₯^3 β π¦^π)/(π₯^2 π¦ + π₯π¦^2 ) (π^3 π₯^3 β γ(ππ¦)γ^π)/(π^3 π₯^2 π¦ +π^3 π₯π¦^2 )=(π₯^3 β π¦^π)/(π₯^2 π¦ + π₯π¦^2 ) (π^π π^π β γ(ππ)γ^π)/(π^π (π^π π + ππ^π))=(π^π β π^π)/(π^π π + ππ^π ) This is only possible when n = 3