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Question

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

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Solution

Given differeential equation is
x(1+y2)dxy(1+x2)dy=0

Separating the variables

x1+x2dxy1+y2dy=0,
Integrating both sides

12log(1+x2)12log(1+y2)=log k

log1+x21+y2=log k2

1+x21+y2=k2, when x=0, y=1

12=k2

(1+x2)=12(1+y2)2(1+x2)=1+y2

y2=1+2x2

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