`(x^(3)y^(2)+xy)dx=dy`

(x^(3)-3xy^(2))dx=(y^(3)-3x^(2)y)dy

Solve: (x^(3)+3xy^(2))dx=(y^(3)-3x^(2)y)dy

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

(x^(3)+3xy^(2))dx+(y^(3)+3x^(2)y)dy=0

y The differential equation of all circles passing through the origin and having their centres on the x-axis is (1)x^(2)=y^(2)+xy(dy)/(dx) (2) x^(2)=y^(2)+3xy(dy)/(dx)y^(2)=x^(2)+3xy(dy)/(dx)y^(2)=x^(2)-2xy(dy)/(dx)

(x^(3)+xy^(4))dx+2y^(3)dy=0

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

The solution of (x^(2)+xy)dy=(x^(2)+y^(2))dx is

(dy)/(dx)=x^(3)y^(3)-xy

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