# Find the particular solution of the differential equation x (1 + y2) dx – y (1 + x2) dy = 0, given that y = 1 when x = 0. - Mathematics

Find the particular solution of the differential equation x (1 + y2) dx – y (1 + x2) dy = 0, given that y = 1 when x = 0.

#### Solution

Given equation can be written as

x/(1+x^2)dx-y/(1+y^2)dy=0

Integrating to get

1/2 log (1+x^2)-1/2log(1+y^2)=logc_1

=>log(1+x^2)-log(1+y^2)=logc_1^2=logc

therefore (1+x^2)/(1+y^2)=c

x=0,y=1=>c=1/2

therefore 1+y^2=2(1+x^2) or y=sqrt(2x^2+1)

Concept: General and Particular Solutions of a Differential Equation
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