Chapter 6.3, Problem 78E

Solving a Homogeneous Differential Equation In Exercises 77-82, solve the homogeneous differential equation in terms of x and y. A homogeneous differential equation is an equation of the form

$M(x,y)dx+N(x,y)dy=0$

where M and N are homogeneous functions of the same degree. To solve an equation of this form by the method of separation of variables, use the substitutions $y=vx\text{and}dy=xdv+vdx$.

$(x^3+y^3)dx-x{y}^{2}dy=0$