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Question

Solve the following
y1+x2+x1+y2dydx=0

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Solution

y1+x2+x1+y2dydx=0

x1+y2dydx=y1+x2

1+y2dyy=1+x2dxx

integrating both sides

1+y2dyy=1+x2dxx

Let y=tanθ,

=1+tan2θtanθ.sec2θdθ

=sec3θtanθdθ

=sec2sinθdθ

=sec2θcscθdθ

=sec2θdθ+csc2θdθ

=tanθcotθ

=y1y

1+y2dyy=1+x2dxx

y1y=(x1x)+c

y21y=1x2x+c

Hence, solved.



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