The general solution of the DE ` 2x y dy + (x ^(2) - y ^(2)) dx = 0 ` isA. ` x ^(2) + y ^(2) = C x `B. ` x ^(2) + y ^(2) = Cy`C. ` x ^(2) + y ^(2) = C `D. none of these

The general solution of the DE ` 2x y dy + (x ^(2) - y ^(2)) dx = 0 `

1.	The general solution of the DE ` 2x y dy + (x ^(2) - y ^(2)) dx = 0 ` isA. ` x ^(2) + y ^(2) = C x `B. ` x ^(2) + y ^(2) = Cy`C. ` x ^(2) + y ^(2) = C `D. none of these
Answer» Correct Answer - A `(dy)/(dx) = (y ^(2) -x ^(2))/( 2x y ) `, which is homogeneous. Put ` y = vx and (dy)/(dx) = v + x (dv)/(dx)`. Then , `int (2v)/(( 1 + v ^(2))) dv = - int (1)/(x) dx rArr log (1 + v ^(2)) = -log x + log C`. `rArr x (1 + v^(2)) = C rArr x ^(2) + y ^(2) =Cx`