Chapter 2.4, Problem 13E

Consider the partially decoupled system
$\begin{array}{l}\frac{dx}{dt}=2x-8y^2\\ \frac{dy}{dt}=-3y\end{array}$

(a) Derive the general solution.
(b) Find the equilibrium points of the system.
(c)Find the solution that satisfies the initial condition $\left(x_0,y_0\right)=\left(0,1\right)$.
(d) Use HPGSystemsolver to plot the phase portrait for this system. Identify (he solution curve that corresponds to the solution with initial condition $\left(x_0,y_0\right)=\left(0,1\right)$ .