Solve: `(dy)/(dx)=(1+y^2)/(1+x^2)`

Answer

`y-x=(1+xy)c`

Explanation

We are given

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


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


Integrating both sides

`int (dy)/(1+y^2)=int (dx)/(1+x^2)`


Using the direct formula `int (dy)/(1+y^2)=tan^(-1)y+c`


`rArr tan^(-1)y=tan^(-1)x+c_1`

`rArr tan^(-1)y-tan^(-1)x=c_1`

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