Separable Equations Example

$$\frac{dy}{dx} = \frac{x^3 - x^2}{y^2}$$

(x³-x²) dx - y² dy = 0

$$\frac{x^4}{4} - \frac{x^3}{3} + \frac{y^3}{3} = c$$

It's not always possible to solve for y, but in this case it is, and we obtain

$$y = (3x^4 - 4x^3 + 4y^3 + C)^{\frac{1}{3}}$$