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

The solution of the DE ` (dy)/(dx) = (( 1+y ^(2)))/((1 + x ^(2))) ` is

1.	The solution of the DE ` (dy)/(dx) = (( 1+y ^(2)))/((1 + x ^(2))) ` isA. ` (y + x) = C ( 1 - yx)`B. ` (y - x ) = C (1 + y x )`C. `y = (1 + x) C `D. none of these
Answer» Correct Answer - B `int ( dy ) /((1 + y^(2))) = int (dx)/((1 +x ^(2))) rArr tan ^(-1) y = tan ^(-1) x + C_1 ` ` rArr tan ^(-1) y - tan ^(-1) x = C_1 rArr tan ^(-1) (( y - x )/( 1+ yx )) = C_1 rArr ( y - x )/((1 + y x ) ) = tan C_1 = C`.