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Solution :

Given that, `(dy)/(dx)=1+x+y^(2)+xy^(2)` <br> `Rightarrow (dy)/(dx)=(1+x)+y^(2)(1+x)` <br> `Rightarrow (dy)/(dx)=(1+y^(2))(1+x)` <br> `Rightarrow (dy)/(1+y^(2))=(1+x)(dx)` <br> On integrating both sides, we get `tan^(-1)y=x+(x^(2))/(2)+k..(i)` <br> When y=0 and x=0, then substituting these values in Eq. (i) we get <br> `tan^(-1)(0)=0+0+K` <br> `Rightarrow K=0` <br> `Rightarrow tan^(-1) y=x+(x^(2))/(2)` <br> `Rightarrow y=tan(x+(x^(2))/(2))`