Pregunta: Solve the given initial-value problem. The DE is homogeneous. xy^2 dy/dx = y^3 - x^3, y(1) = 3

$\mathrm{A}\mathrm{N}\mathrm{S}\mathrm{W}\mathrm{E}\mathrm{R}:$

The given differential equation is $\mathrm{x}{\mathrm{y}}^2\frac{\mathrm{d}\mathrm{y}}{\mathrm{d}\mathrm{x}}={\mathrm{y}}^3-{\mathrm{x}}^3,$ with the initial condition $\mathrm{y}\left(1\right)=3.$

To solve this homogeneous differentia...