Find a particular solution of the differential equation: `(x+y)dy+(x-y)dx=0; y=1\ w h e n\ x=1`

Answer

`2 tan ^-1(yx)+log (x^2+y^2)=pi/2+log 2`

Explanation

We have


`(x+y)dy+(x-y)dx=0`


Simplifying,


`rArr (x+y)dy=-(x-y)dx=0`


`rArr (x+y)dy=(y-x)dx=0`


`rArr (dy)/(dx)=(y-x)/(y+x)-(1)`


Put `y=v x`


Differentiating we get,


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