Chapter 9: First-Order Differential Equations - Practice Exercises - Page 557: 15

$xy=-y^3+c$

Here, we have $x dy+y dx=-3y^2 dy$ The general solution can be determined when we multiply the equation $x dy+y dx=-3y^2 dy$ with the integrating factor and then integrate on the both sides. we have $\int [xy]' =\int -3y^2 dy$ This implies that $(xy)=-(y^3)+c$ Hence, $xy=-y^3+c$