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Solution :

`(1+x)(1+y^(2))dx+(1+y)(1+x^(2))dy =0` <br> `rArr ((1+x))/((1+x^(2)))dx +((1+y))/((1+y^(2)))dy =0 " " `[on seperating the variables] <br> `rArr int ((1+x))/((1+x^(2))) dx + int ((1+y))/((1+y^(2)))dy =C " " `[integrating both sides] <br> `rArr int{(1)/((1+x^(2))) +(x)/((1+x^(2)))}dx + int{(1)/((1+y^(2))) +(x)/((1+y^(2)))}dy =C` <br> `rArr int(1)/((1+x^(2))) dx +(1)/(2)*int(2x)/((1+x^(2))) dx +int(1)/((1+y^(2)))dy +(1)/(2)*int(2y)/((1+y^(2))) dy=C` <br> `rArr tan^(-1)x +(1)/(2) log(1+x^(2))+tan^(-1)y+(1)/(2)log(1+y^(2))=C` <br> `rArr tan^(-1)x +tan^(-1)y +(1)/(2){log(1+x^(2))+log(1+y^(2))}=C,` <br> which is the required solution.