The general solution of the DE ` x ^(2) (dy)/(dx) = x ^(2) + xy + y ^(2) ` isA. ` tan ^(-1) ""(y)/(x) = log x + C `B. ` tan ^(-1)""(x)/(y) =log x + C `C. ` tan ^(-1) ""(y)/(x)=log y +C `D. none of these

The general solution of the DE ` x ^(2) (dy)/(dx) = x ^(2) + xy + y ^(

1.	The general solution of the DE ` x ^(2) (dy)/(dx) = x ^(2) + xy + y ^(2) ` isA. ` tan ^(-1) ""(y)/(x) = log x + C `B. ` tan ^(-1)""(x)/(y) =log x + C `C. ` tan ^(-1) ""(y)/(x)=log y +C `D. none of these
Answer» Correct Answer - A ` (dy)/(dx) = d ( x ^(2) + xy + y ^(2))/( x ^(2))`, which is homogeneous. Put `y = vx and (dy)/(dx) = v + ( dv)/(dx) ` to get ` v + x (dv)/(dx) = (1 + v + v ^(2))` ` therefore int (dv)/((1 + v ^(2))) = int (1)/(x) dx rArr tan ^(-1) v = log x + C rArr tan ^(-1) ""(y)/(x) = log x +C`.