Chapter 2.1, Problem 20P

In each of Problems $13$ through $28$:

(a) Find the solution of the given initial value problem inexplicit form.

(b) Plot the graph of the solution.

(c) Determine (at least approximately) the interval in which the solution is defined.

$\frac{dy}{dx}=x^2{e}^{-3y},y(2)=0$