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

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

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

Show that the differential equation representing one parameter family of curves (x^(2)-y^(2))=c(x^(2)+y^(2))^(2)is(x^(3)-3xy^(2))dx=(y^(3)-3x^(2)y)dy

Prove that x^(2)-y^(2)=c(x^(2)+y^(2))^(2) is the general solution of differential equation (x^(3)-3xy^(2))dx=(y^(3)-3x^(2)y)dy, where c is a parameter.

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

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