The solution of ` (dy)/(dx) = 1+ y + y^(2) + x+ xy + xy^(2)` isA. `tan^(-1)((2y+1)/(sqrt(3)))=x+x^(2)+C`B. ` 4 tan^(-1) ((4y+1)/(sqrt(3)))= sqrt(3)(2x+x^(2))+C`C. ` sqrt(3) tan^(-1) ((3y+1)/3)=4 (1+x+x^(2))+C`D. ` 4 tan^(-1) ((2y+1)/(sqrt(3)))= sqrt(3)(2x+x^(2))+C`

The solution of ` (dy)/(dx) = 1+ y + y^(2) + x+ xy + xy^(2)` isA. `tan

1.	The solution of ` (dy)/(dx) = 1+ y + y^(2) + x+ xy + xy^(2)` isA. `tan^(-1)((2y+1)/(sqrt(3)))=x+x^(2)+C`B. ` 4 tan^(-1) ((4y+1)/(sqrt(3)))= sqrt(3)(2x+x^(2))+C`C. ` sqrt(3) tan^(-1) ((3y+1)/3)=4 (1+x+x^(2))+C`D. ` 4 tan^(-1) ((2y+1)/(sqrt(3)))= sqrt(3)(2x+x^(2))+C`
Answer» Correct Answer - a Given, ` (dy)/(dx) = (1+y+y^(2))+ x(1+y+y^(2))` ` = ( 1+ y + y^(2)) (1+x) ` ` rArr = (dy)/(1+y+y^(2)) = (1+x)` ` rArr int (dy)/((y+1/2)^(2)+((sqrt3)/2)^(2)) = int (1+x)dx` ` = (1+y+y^(2)) (1+x)` ` rArr (dy)/(1+y+y^(2)) = (1+x)dx` ` rArr int (dy)/((y+1/2)^(2)+((sqrt(3))/2)^(2) )= int (1+x)dx` ` rArr 1/(sqrt(3)/2) tan^(-1) ((2y+1)/(sqrt(3))) = sqrt(3) (2x +x^(2)) +C`

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