`xy(dy)/(dx)-y^(2)=(x+y)^(2)e^(-(y)/(x))`

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

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

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

(dy)/(dx)=(x^(2)-y^(2))/(xy)

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

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

Solve the differential equation _(y-3)(dy)/(dx)=((x+1)^(2)+(y-3)^(2)e^((y-3)/(x-1)))/((xy-3x+y-3)e^(x+1))

The differential equations of all circle touching the x-axis at orgin is (a) (y^(2)-x^(2))=2xy((dy)/(dx)) (b) (x^(2)-y^(2))(dy)/(dx)=2xy ( c ) (x^(2)-y^(2))=2xy((dy)/(dx)) (d) None of these

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

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