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

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

Solve: x+y dy/dx=(a^2((x dy/dx-y))/(x^2+y^2))

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

Solve: x+y dy/dx=(a^2((x dy/dx-y))/(x^2+y^2))

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

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)

(x-y)dy-(x+y)dx=0

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

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

Solve the following differential equations: (dy)/(dx)=1+x+y+x y (ii) y-x(dy)/(dx)=a(y^2+(dy)/(dx))