Chapter 8.3, Problem 23ES

(a) Find a slope field whose integral curve through (1, 1) satisfies $x{y}^3-x^{2}y=0$ by differentiating this equation implicitly.

(b) Prove that if $y\left(x\right)$ is any integral curve of the slope field in part (a), then $x{\left[y\left(x\right)\right]}^{\text{3}}-x^{2}y\left(x\right)$ will be a constant function.

(c) Find an equation that implicitly defines the integral curve through $\left(-1,-1\right)$ of the slope field in part (a).