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

General solution of (x^(3)y^(2)+y^(2))(dy)/(dx)+(x^(2)y^(3)+x^(2))=0 is

(x^(2)-x^(2)y)(dy)/(dx)+y^(2)+x^(2)y^(2)=0 A) x-(x^(-1)+y^(-1))-logy=c B) x+(x^(-1)-y^(-1))=log(cy) C) x^(2)+xy+log((y)/(x))=c D) (x^(-1)-y^(-1))+logy=x+c

The solution of the differential equation x=1+xy(dy)/(dx)+(x^(2)y^(2))/(2!)((dy)/(dx))^(2)+(x^(3)y^(3))/(3!)((dy)/(dx))^(3)+...is

Solve: (x^2+2xy+y^2+1)(dy)/(dx)=2(x+y)

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)

The solution of x^(2)+(y^(2)dy)/(dx)=4 is x^(2)+y^(2)=12x+Cb*x^(2)+y^(2)=3x+Ccx^(3)=y^(3)=3+Cd*x^(3)+y^(3)=12x+C

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

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

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