`(dy)/(dx)=(y(xlny-y))/(x(ylnx-x))`

(dy)/(dx)=(y-x)/(x+y)

y-x(dy)/(dx)=x+y(dy)/(dx)

(dy)/(dx)=(y)/(x)-tan""(y)/(x)

The solution of (dy)/(dx) = (x-y)/(x+y) is

Express (dy)/(dx)=(y)/(x+ye^((-2x)/(y))) in the form (dx)/(dy)=F((x)/(y)).

(dy)/(dx)=(y)/(x)+cot""(y)/(x)

(x-y)(dy)/(dx)=x+3y

If y=x log((x)/(a+bx)), thenx ^(3)(d^(2)y)/(dx^(2))= (a) x(dy)/(dx)-y (b) (x(dy)/(dx)-y)^(2)y(dy)/(dx)-x(d)(y(dy)/(dx)-x)^(2)

y^2+x^2(dy)/(dx)=x y(dy)/(dx)