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

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

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

The first integral of (dy)/(dx)((d^(2)y)/(dx^(2)))-x^(2)y((dy)/(dx))=xy^(2) will be

If xy log(x+y)=1, prove that (dy)/(dx)=-(y(x^(2)y+x+y))/(x(xy^(2)+x+y))

xy log(x+y)=1, prove that (dy)/(dx)=-(y(x^(2)y+x+y))/(x(xy^(2)+x+y))

If xy log(x+y)=1, prove that (dy)/(dx)=-(y(x^(2)y+x+y))/(x(xy^(2)+x+y))=

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

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

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

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