[" 78.The solution of "],[qquad (x^(3)-3xy^(2))dx=(y^(3)-3x^(2)y)dy]

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

Solve: (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.

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

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

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